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?

What do you recommend for:
AntiVirus
Spyware
Disc Defragmentation
Cleanup
etc.
???