There is no Jon Snow. How Lyanna dies I will leave it up to you to do decide? Comment it in the comments.
Ned marries Ashara instead of Catelyn. Arthur Dayne still dies though.
Aegon Martell's head is smashed into the ground and dies, but Elia Martell and her daughter Rhaenys are saved by timely intervention of Ned, who convinced Robert somehow to let the girl Targaryen who looked more Dornish to live.
What happens to Dany's mother, I leave up to you. Personally I want her to live so chose a proper story line around this and comment.
What happens to Viserys I leave it to you as well.
The eldest son of Stark is MC, who is the same age as canon Jon. Then three years later, Robb is born, followed by Sansa two years later