We can put a wrap on this problem. I'll go through the process, though, for those who search the archive for similar problems.
Apple thought I had a bad card. I went to a nearby Mac reseller. They plugged in a new card and still no go. I tried to go through the simple answers. It turned out, as it often does with Macs, that it was indeed a simple answer.
Turns out that the extensions for Airport were off. Why? Remember that I once had an Airport card in this machine. When the card was taken out, the extensions for Airport were turned off. When the new card went in, and new software was installed, no new extensions were installed -- either because these are installed by the system software, or because the Airport software sees that extensions are already there and does not install new ones.
Normally, when you install software, you don't check the Extensions folder because you assume that whatever extensions are put in there they will be "on".
When I got the machine home I still had difficulty connecting to the Netgear router -- but these issues were worked out in short order and I am now wireless with this Mac.