I do not have a firewall as such but am running Norton Internet Security 2003, which of course includes Norton AntiVirus. My PC is not on a network. It is running Windows Me.
Spud, wellcome to avast forums.
Generally speaking, you cannot have two resident active antivirus applications in your system. They will conflict.
For sure, NAV 2003 (or 2004) conflicts with avast and viceversa.
I used NAV in the past but give up for avast. I think you must choose one of them. Probably, you can stay with the firewall of Norton Internet Security but I'm not sure.
You will find here a lot of users that claims for 'layered protection': different applications that do, each one, its part on security. Symantec, on contrary, joins all applications in only one.
You won't regret using avast!