Could be a number of things and very hard to say by remote.
Could be that it's lost the WEP/WPA pass key. Are you sure it's really connecting to the access point? It might look like it's connected but if it doesn't have the right key it will never work of course.
What do I do to check the pass key?
It should be DHCPing an IP from the WRT54G. Do you know that's happening? Right click->Status on the systray icon or in Network Connections.
I did that, but I don't know where to look for the IP from the WRT54G. It just says "Connected", 100 Mbps (since I disabled wireless and connected directly with Ethernet), and shows a number of packets sent/received. Clicking on "Properties" and "Configuration" gives a dialog box that says "This device is working properly." I assume that "device" is the WRT54G?
If so, AVG hasn't found it.
Do you know if your WRT54G has an IP 192.168.1.1? If so, Start->Run->CMD and the run "ping 192.168.1.1".
Apparently it does. (see attached photo)
Whilst you are there at the command prompt, run "ipconfig /all" Given you don't have a working network, perhaps take a photo and post?
See attached photo
Direct Ethernet is a good start and rules out things like IE playing up. More than likely I suspect a network config issue.
Hopefully you can see something in the attached photos that will give a clue.
Don't be too critical of the photo quality. I live (literally) in a glass house with bright sunlight streaming in and lighting up the very reflective screen on the netbook. Makes things difficult...

tanstaafl.