This is a loaded subject for obvious reasons. I am not a mind reader and I am certainly not in GRRM's confidence. By necessity, everything in this article is based on speculation. I use hints in the novels as well as the early submission he gave to his editor in drawing these conclusions.
Disclaimer given, let's continue.
This article is what I believe GRRM was ORIGINALLY going to write when he first began his ASOIAF 'trilogy'. This is what it may have looked like had he stuck to his original conception and did not allow his imagination to run wild.
What you will notice is that there are considerably fewer characters than in the finished books. The personality of most of the characters is different. Events will not play out the same way, but many of the conclusions will be. Finally, there are going to be plot holes. This is because it was the need to fill these holes which is why Martin started to change his story in the first place. It is ironic that without these holes in his original story we wouldn't have gotten the grand epic that so many people have fallen in love with.
I will not go into anything that is the same in both versions beyond mentioning when an event takes place.
The beginning is easy enough. No changes are necessary. It is only when move toward the middle of the first novel, A Game of Thrones, that the alterations start. From this point forward I am simply going to relay what the probable storyline was, not make comparisons as to how it is now. Bare in mind that the story moves much faster as it was intended to be strictly a trilogy.
We will begin with where Arya runs away after wounding Jeoffrey. She does not return but attempts to journey back to Winterfell. Only she gets lost. Robert allows Ned to search for his daughter for only a few days before losing patience and continuing his journey. Ned is forced to go with him, leaving some of his men to continue the search.
When Catelyn gets word of Arya's disappearance, that combined with the attempt on Bran's life, causes her to rush south herself to try and find Arya. She meets Ned's men and joins them. They encounter Tyrion on his way south to Kings Landing and arrest him. She takes him to the Eyrie, where she has a very disturbing interview with her sister Lysa. Catelyn leaves to resume her search but Lysa is less than interested in keeping Tyrion under lock and key. He is able to bribe his way out and runs for Kings Landing.
While wandering the Riverlands, Arya helps a man escape execution. The man introduces himself as Jaqen H'gar, one of the Faceless Men. He was returning to Braavos when he was captured but the circumstances of how are mysterious. He agrees to teach Arya how to kill to reward her for saving his life.
After joining the Night's Watch, Jon goes with Lord Commander Mormont north of the Wall to investigate reports of the Others. Jon saves Jeor's life and is made his bodyguard and personal steward. Despite this Jeor is murdered by his own men, who want to abandon the Wall and flee south. With the Watch in chaos, Jon is able to rally the loyal men to put down the mutineers. He is elected as the new Lord Commander.
Events at Kings Landing largely remain the same, with Ned meeting Littlefinger and finding Robert's bastard son Gendry. Cersei, in connivance with Littlefinger and Renly, murder Robert. Sansa, who wants to marry Jeoffrey, betrays Ned when he plans on fleeing the city. She is rewarded with a marriage to Jeoffrey. Renly flees when he realizes Cersei double-crossed him.
Jeoffery has Ned executed.
Daenerys hates her new husband Drogo. Despite her poor relationship with her brother, she is enraged at Drogo's treatment of him. When Drogo's Khal arrives at Vaes Dothrak Quaithe is there to meet them. She is able to convince Daenerys to become her student and shows her several visions.
Drogo kills Viserys in a moment of peak. Daenerys uses the new powers Quaithe taught her to subdue Drogo. She then burns him alive on her brother's pyre. As a result the eggs hatch and she becomes the Mother of Dragons. The dothraki bow to her as their new god.
Varys convinces Young Griff, aka: Aegon Targaryen/Blackfire, to seek out Daenerys and marry her. She has since marched on the cities of Slavers Bay, swearing to free all the slaves. He attempts to win her over but she laughs in his face. She knows he isn't her nephew because he is younger than she is. He leaves swearing to conquer Westeros himself.
Quaithe leaves Daenerys giving her one final vision of warning. She never returns.
Renly joins the Tyrells and they march on Kings Landing. When word reaches Winterfell of Ned's execution Robb calls the banners. He sends Theon to treat with his father to bring the Ironmen into the war on Robb's side. But Theon finds that his father was murdered by a Faceless Man, ie: Jaqen, and his uncle Euron now rules. Euron imprisons and tortures Theon.
Euron invades the North after Robb takes his army south of the Neck.
The approach of the Tyrell army causes the Hound to flee Kings Landing. At the last minute the Tyrells switch sides and join Tywin, who was also marching on Kings Landing. Renly runs to Robb. Catelyn has rejoined Robb by then, her search proving fruitless.
After teaching her what he knows Jaqen leaves, exiting the story. But Arya is then caught by the Hound who wants to ransom her back to her brother. Catelyn and Robb have made an alliance with the Freys with a marriage between Robb and Walder Frey's youngest daughter. But Robb hates the Freys and has a dalliance with another girl.
Unknown to Robb, Walder has schemed with Renly to betray Robb. At the wedding the Frey's murder Robb and his army. Renly marries Walder's daughter himself. Catelyn escapes only to run into the Hound and Arya on their way to the Twins. The three head north to get back to Winterfell. The Hound agrees to teach Arya how to fight along the way. He eventually declares her the best warrior Westeros has ever seen.
Bran and Rickon are forced to flee an undefended Winterfell when the Ironborn attack. They join up with Arya's group and head north to the Wall. Bran manages to convince them they need to go beyond it to find the Three-Eyed Crow. Catelyn agrees only because she refuses to beg for help from Ned's bastard.
Sansa is pregnant with Jeoffrey's child. Littlefinger tricks her into drinking moontea and she miscarries. Using this as a pretext, the Lannisters set aside her marriage to Jeoffrey and he marries Margaery Tyrell instead. He is poisoned at his own wedding and Sansa is suspected. Littlefinger flees with her to the Eyrie where Lysa is waiting for them. Sansa realizes Lysa was in on the it the whole time.
Jamie convinces Cersei that their brother Tyrion was responsible for Jeoffrey's death. Tyrion demands a trial by combat. The Red Viper, who wants revenge against the Lannisters, agrees to be his champion. The Mountain kills Oberyn but not before taking a poisoned wound. He himself dies afterward. A defrocked maester, Qyburn reanimates the body to be a bodyguard for Cersei. Before his execution Jamie helps Tyrion to escape. Before leaving Tyrion confronts his father Tywin, who admits that Tyrion is not actually his son but is the bastard child of Aerys. In a fury Tyrion murders Tywin. Ironically, Tywin was the one person whom Jamie truly cared about and he swears vengeance against Tyrion.
In reality it was Jamie who murdered Jeoffrey. He locks his and Cersei's other two children, Myrcella and Tommen in the Tower of the Hand, with the pretext of protecting them, and the two are never seen again.
Jamie declares himself Protector of the Realm. Cersei thinks he is going to marry her but he marries Margaery instead.
Stannis, who has been sitting on Dragonstone the whole time, is persuaded by Melisandre to go north to protect the Wall. He arrives just in time to save the Night's Watch from Mance Rayder. Despite Jon's pleas, Stannis decides to sacrifice Mance to the Red God. Jon is murdered by his Watch brothers for allowing the Wildlings south. When Mance is burned Jon is suddenly resurrected. The Wildlings declare him their god and Stannis makes him his second.
Tyrion reaches Daenerys. She is skeptical of his claims of being her brother. But when he manages to tame one of her dragons she makes him her second, much to Jorah's displeasure. They discover that Tyrion also has a talent with magic and Daenerys appoints herself his teacher.
When Euron hears about Daenerys being in Slavers Bay he decides the time has come to claim her. He is also influenced by the invasion of the Golden Company. He offers her marriage and will transport her army to Westeros. She is completely taken with him and agrees, only realizing too late that she is his prisoner.
With Euron in Essos, Theon's sister Asha helps him to escape and they make their way to Winterfell. They find the garrison there loyal to Asha. Stannis, with his combined army of Southrons and Wildlings, is marching on Winterfell. Asha tries to make a deal with him but Stannis refuses.
Renly is told by Varys that Walder has betrayed him. Renly flees north to his brother, only to have Stannis sentence him to death for being a traitor.
Sansa tricks Littlefinger into betraying himself and she has him thrown out the Moon Door. She is now the Lady of the Vale as Littlefinger had already murdered Lysa.
A battle takes place outside of Winterfell with Stannis' army victorious. But Stannis himself has disappeared and his body is never found. Jon now finds himself in command of the army. He has also captured Theon and Asha. He keeps Theon as a hostage but sends Asha back to try and turn the Iron Islands against Euron.
Bran's group manages to find the Three-Eyed Crow but are themselves discovered by the Others. Bran is unable to learn much from the Crow before he is killed. Catelyn is also killed. She returns as a wight and Arya is forced to slay her. She starts having second thoughts about her quest for revenge.
They flee to the Wall. Bran is unable to follow and his body is killed. His friends don't know it but he has transferred his mind into the weirwoods. The group is able to get through the Wall but are unable to stop the wights from following. Bran is forced to use Hodor to 'hold the door'. The group escapes south but the Others are able to break into the tunnel under the Wall.
Rickon loses himself inside his wolf Shaggydog and the others are forced to kill him.
Faegon has invaded Westeros with the Golden Company. Dorne and much of the Reach join him. He is able to destroy the Tyrell army and marches toward Kings Landing. Kings Landing is in revolt for Jamie is despised. The Tyrells, unable to get support from Jamie, flee to the Sept of Baelor. Cersei, in order to get rid of Margaery, has Zombie Mountain ignite the wildfire under the Sept. Much of Kings Landing is destroyed.
Euron's fleet arrives at Oldtown. Euron promptly sacks it with help from Tyrion. Daenerys plots to escape Euron but ill advisedly tells Jorah. Jorah betrays her to Euron. Word of her imprisonment reaches Winterfell. Arya and the Hound have also reached Winterfell. Knowing he needs the dragons to stop the Others, Jon agrees to allow Arya an attempt to rescue Daenerys. As she travels south she murders Walder Frey on the way. Arya succeeds in freeing Daenerys. Daenerys is able to once again take flight and burns the Iron Fleet, along with Jorah and Euron.
Jon travels south to meet Daenerys. His people have been forced to flee the North. Bran comes to Jon in a dream and tells him his true parentage. Jon refuses to believe. Daenerys also refuses to believe when he tells her. She forces him to face the dragons and he is able to tame one. Thus he becomes the third dragon rider.
They face Faegon's expanded army as they march north. Faegon has taken most of Westeros south of the Neck except Kings Landing and Casterly Rock. In a battle reminiscent of the Field of Fire, the three dragon riders attack from above while Arya leads the army below. She has impressed them all with her natural leadership. Faegon is killed. Varys is captured and also killed. Doran, the Prince of Dorne is murdered by his nieces, the Sand Snakes, and they take control of Dorne.
Sansa journeys to meet them. She offers to ally with them if she can marry Jon. Daenerys refuses and Sansa allies with them anyway.
Tyrion and Arya seize Casterly Rock. Tyrion has fallen hard for Arya. This is bad because Jon was already in love with Arya. A love triangle develops. Tyrion asks Daenerys to marry him to Arya. Daenerys agrees because she wants Jon to marry her and he doesn't want to. Arya is utterly against marrying Tyrion and she goes to Jon. Jon supports Arya. The two former friends now duke it out, with their dragons. Tyrion, using his magic, looks like he is going to win. But Jon demonstrates a power no one else ever had. He takes control of Tyrion's dragon, showing he can take control of any dragon. Daenerys now agrees to set aside a marriage between Tyrion and Arya. She will allow Jon to marry Arya but only if he marries her too.
Tyrion, enraged, denounces Daenerys and flees to Kings Landing. Jamie is not happy to see him and throws him in the dungeon. Tyrion is able to convince Cersei that it was really Jamie who murdered Jeoffrey.
Jon sends the dragons against the Others. To everyone's surprise, the dragons lose. The Others freeze Viserion to death. Daenerys will not allow the dragons to be put at risk again.
Unseen and unheard by mortals, Bran has discovered the Heart of the Weirwoods. And it is the Heart which is responsible for the Others. Knowing victory for the Others would mean death for all of Westeros, Bran fights a psychic battle against the Heart. After a fierce struggle he wins. The clouds covering Westeros, a result of the magic of the Heart without which the Others could not move, dissipate. Without the clouds the Others die.
Believing the war is won, Jon send the army against Kings Landing. Jamie though has anticipated this. He sends forth his monster - an undead dragon made of the bones of the ones in the Red Keep. Qyburn created it. It bursts forth from the tower, killing Rhaegal. Drogon smashes it, though not before he himself takes a poisoned wound. In the battle inside the city itself the Hound is able to lure his zombie brother into a trap using wildfire.
During the fight Cersei comes to Jamie and tells him what Tyrion said. Jamie doesn't even bother to deny it. Cersei inflicts a mortal wound on Jamie but he is able to strangle her to death before he dies. Tyrion escapes.
In another dream, Bran tells Jon he still has another task to perform. He must destroy the Weirwood Heart. Otherwise it will only recreate the Others again. With Bran's help, Jon flies a dying Drogon to the Fist of the First Men, which is actually a giant weirwood covered by a glamor. Drogon burns down the tree but dies afterward.
The seasons of Westeros return to normal. Most of life also appears to return to normal. Except it hasn't. Jon duly marries Arya and Daenerys and is crowned king. Daenerys is found to be with child. But Sansa has never forgiven Daenerys for preventing her from becoming queen. With Tyrion's connivance, she tricks Daenerys into drinking moontea. Daenerys goes into premature labor and suffers sever loss of blood. She is left with the mind of a child. Her son has no mind at all.
Jon, who blames himself and believes he's cursed, takes Daenerys and vanishes, never to be seen again. Jon having no other relatives, Arya finds herself Queen of Westeros. A position she manifestly doesn't want. Unwilling to execute her only living relative, she exiles Sansa to the Eyrie, forbidden any and all visitors. Arya swears never to marry again.
Unknown to all, Bran skinchanges Jon's son, giving himself a second life and knowing he will one day grow up to be King of Westeros.
At the end of the story we see Tyrion boarding a boat, exiled and attainted, forbidden from ever returning. He is embarking on a hopeless quest to find his long lost wife.