I just wanted to thank the person in the chain below who proposed the following solution to get Firefox & IE working again on an old computer (XP) that does in fact have internet connection.
After trying everything else, this is what worked:
"Just wanted to say thanks for all the suggestions. The machine I use has XP
I clicked on Network Connections, right clicked on the wireless network connection, scrolled down to TCP/IP, clicked on the label to highlight it, clicked on properties, clicked on obtain IP address automatically (obtain DNS server address automatically is automatically selected), clicked on ok and all worked like as advertised.
My primary clue to pursue this avenue was observing that the DNS was not being created when I reset the wireless connection (create a new network or add a device to an existing network).