The replacement Wireless adapter card arrived today. I put it in, and I was able to view my wireless network, but was still not able to connect to it. Then I realized that I had MAC Filter security turned on, and maybe the address of the new adapter was different from the old address. I checked it, and sure enough, the address was different. So I added the new address to the list, and now I'm up and running perfectly!
Thanks for all of your help.