I doubt you have only Norton Anti Virus installed since NAV can't possibly affect internet access.
More likely you have Norton Internet Security installed, which includes a firewall. Besides being one of the buggiest and most code bloated pieces of garbage ever written by Symantec, it's a marvelous program.
Could be someone accidently locked down the Norton firewall.
If it turns into a hassle to diagnose, and if this is an older computer, uninstall Norton, turn on the Windows XP firewall and install one of the free anti-vurus programs out there like AVG or AntiVir. Anything's better than Norton's bloatware.
Hope this helps...