OT Mechanics, need some advice

My father in-law has a 2003 GMC Yukon XL. He went to go to work on Monday and as soon as he put the key in the on position the starter motor kicked on and then wouldn't stop trying to turn over even after the car had turned on (he didn't even turn the key to crank it, he just put the key in the on position).

So, yesterday we changed the starter motor. We had the key in the on position because i had turned the wheel to get a better angle, and when we finished and went to reconnect the battery it immediately started trying to turn over.

Has anybody here come across a similar problem? I've never seen anything like it. I've tried searching online, but while i can find plenty of people who have starter motors that won't work at all, i can't find anybody who's had one that kicks on without being cranked and won't turn off.