Remove Norton serial code

My previous subscription to Norton 360 expired, so I got a new one. The problem is that the previous one has been logged somewhere on my computer, because when I try to re-install it doesn't ask me for a serial code and just ends up expired.
So how do I delete it and use my new one?

>>7
1) backup the files
2) delete the files from the computer
3) restore the backup
4) computer is defragmented