Yes. You can uninstall Norton and should. BUT, Norton won't fully uninstall. To complete the task do it manually, following these instructions:
http://www.pcworld.com/howto/article/0,aid,117824,00.asp

You also want Sygate firewall, downloadable from:
http://smb.sygate.com/
When you first go on the net leave the windows firewall on and turn it off only after Sygate is up and running.

The question is not, Can they reason? nor, Can they talk? but, Can they suffer?
~Jeremy Bentham