I seem to be in the minority here, but I actually do use and appreciate Norton!
As for the problem mentioned, when you reinstall a new version of Firefox Norton sees this as a 'changed' program and needs your consent whether to allow it internet access. Judging by the symptoms it is now blocked. To change this you don't need to add it again, go to the list of programs (somewhere under the firewall settings, I'm at work and cannot check this) and find Firefox in this list. On the right is the setting for this program and I would guess that it will say 'blocked'. Change this to allow access and you should be sorted.
Obviously some of the suggestions above will also have the same effect. Since you've been switching NIS off it might be worth scanning your system to see if anything nasty has crept in.