Get rid. Norton is a horrible piece of lardy bloatware which seems to get worse every year. AVG is a perfectly capable anti-virus, and for most cases the built-in XPSP2 firewall is more than adequate. Hell, Norton can't even uninstall itself a lot of the time, hence Symantec had to release a utility to do it!
This here laptop sits on the side in our kitchen for general use, never gets switched off, has a public IP address, AVG and the XP firewall. Problems? None.