I have Norton Internet Security 2005 and have not had problems except with CDDB with a proxy server.
Assuming you are using the Norton forewall, but something should work with other firewalls.
As suggested, try turning off NIS briefly and see if you can connect then. If you can try the following:
Make sure you have all updates.
Go in to the firewall settings - configure programs.
Delete references to itunes and quicktime. You may find them listed under Apple.
Restart the computer.
Then go into the firewall and manually configure these programs:
In Program Files\iTunes - iTunes.exe and iTunesHelper.exe
In Program Files\Quicktime - QuicktimePlayer.exe, qttask.exe and QTInfo.exe.
In fact for me the automatic configuration worked fine, but doing it manually seems to have worked for some people.
Another thing that can cause connectivity problems, go into Internet Explorer Tools>Internet Options>Connextions>LAN Settings and make sure that "Automatically detect settings" is checked.