UPDATE: Apparently it was the Norton Internet Security that was causing the problems. Some of you will no doubt not be surprised.
I uninstalled the NIS, and the started the Firefox browser. It connected and worked normally. However, I am not comfortable running my computer without an internet security program, so reinstalled the NIS. Everything is now working as it should.
As an interesting side note, this computer is only a couple of months old. It is a Dell XPS 400. I got out the Norton Internet Security reinstall CD, and I noticed that the product code on the sleeve was different than the one that came up on the computer when I checked it. I reinstalled the NIS, and when I registered it, I had to enter a product key. The one originally in the computer did not work (it came back as invalid).
So I had to use the product key on the reinstallation CD sleeve. I was hoping to use the other product code until the original 15 month subscription to updates ran out. I don't know why Dell supplied a reinstallation CD with a different product key than the one originally installed in the computer at the factory, but then again this computer's operating system is XP Media Center, and the operating system reinstall CD is XP Pro!