It is better to freshly install it on your new PC. Just register it again with the same name/address as before. It will give you the added benefit of getting a whole 12 months free updates again
You should be able to just re-install it on your new PC and register it with your current username and registeration code as before. If you have any other problems with this, you might want to give Norton support a call and they will be able to tell you for sure what you need to do.