I just fixed my own problem. See below, because when I re-install anti-virus, I expect a possible recurring issue.
I have my Mom's IBM Netvista (2292-21U) (P4 1.6GHz, 640MB RAM) with Windows XP SP2. I needed to connect to the web to patch it and do some general cleanup. She normally uses AOL dial up, but I have cable internet with a Netgear router and a wired connection. I had her up and running and I applied patches, but then I started messing with processes and services to speed up performance. I also think I partially removed Norton 360. Somewhere along the way, I lost connection. Symptoms were that Windows networking showed a connection and an assigned IP, and it showed the gateway. But neither IE7 nor Firefox 3 would connect, and doing a Ping from Cmd Prompt did not work to the gateway or other computers on the network. After googling many sites on the problem and releasing the DNS, etc, I was frustrated because nothing seemed to work. This morning I downloaded Norton Removal Tool and ran it. Now I can see the web. I reinstalled Symantec, this time with Symantec Endpoint Protection. I am still connected. Does Norton have some logic built into their software that if part of the software is disabled, it disconnects the web? It sure seems so.