Point one. They will not run together, you would need to uninstall your current version.
Point two. Norton stuff tends to take over and is IMHO to be avoided
Point three. Gandalf is 100% correct. Free AV and Firewalls available all over. AVG, sygate, Zone Alarm etc etc. AVG is great. Z A is also great, just do not put Zone Alarm 5 on your machine until they iron out the bugs, find a 4.5 build from the net or a cover cd.
I upgraded to Norton Internet Security 2003 last year, previously had Norton System works 2002 including the anti-virus & firewall. Was able to keep the Systemworks and the internet security which actually merged with this. Not really an upgrade as you need to delete the previous anti-virus and firewall, was a bit tricky to sort out as you need to check all of the previous versions deleted (see Symantec website). You cant run two firewalls together. Have tried AVG and F-Secure antivirus but never really as happy with them. Best Antivirus freeware according to recent PC utilities was AntiVir 6.21.09.20 at click here but not as good as paid versions.