It sounds like you feel the only mistake you made was getting caught.
If I accidently had an piece of merchandise in my pocket while walking out the store, then I should get a second chance.
If I STOLE a piece of merchandise, got caught, got banned from the store, the merchant has EVERY RIGHT to NEVER LET ME BACK IN AGAIN.
Google has already see your character. You had no problem stealing when you thought you were going to get away with it. Only when you got caught did you stop. That is not the type of person I want to spend my adword money on.