What if Ned became King instead of Robert?

So this question has been on my mind for years. I know Robert was chosen to be King because he had a distant relative that was Targaryen. But the whole point of the rebellion was because Rhaegar “kidnapped” Lyanna Stark and the Mad King killed Richard Stark and Branden Stark (Ned’s father and older brother).

So what if Ned became King instead? How would things differ?