Serial Number

is there a way to get a Serial Number to confirm a purchase, without email or the application. 

long story short i thought i confirmed it a long time ago, guess i didn't, and recently i had to change my hard drive, i went to use my backup. But to my surprise it said i needed to but in the Serial Number, which is lost long ago in my email. and my fried hard drive, so is there anyway to get it?