I don't know if it's different in college, but in High School, if an ineligible player appears in the game, you have to forfeit the game. It doesn't matter what the player did in the game. If he just ran down the field on a kickoff, but was ineligible, that is a violation.
In my experience covering HS sports, this comes up in transfer situations. I know of a couple of situations in recent years in SW MN where schools have had to forfeit multiple games after using a player who should not have been eligible.
Again, don't know the college rule, but in HS, the school and AD are presumed to know and follow the rules, so you can't plead ignorance. ineligible is ineligible. can't say "gee, we didn't know."
But in my experience, there are set penalties for a rules violation. it's not a Chinese menu. you don't get to pick one from column A or one from column B.