Took two laptops to workplace #2 today. The Thinkpad T41 has an Intel 2200 B/G card on XP and has connected with no issues at workplace #1. It would not connect properly at workplace #2, which has just gone wireless a couple of months ago with two expensive D-Link gigabit routers. I changed the Broadcom driver in the X31 on Win 7 to one that I'd found that claimed to also cover Win7 and it finally worked! Previously it had not worked at #1. So now the situation with those two laptops and wireless cards at workplace #2 is the reverse of workplace #1. My only guess is that the issue may now be encryption. I think workplace #2's newer routers are WPA2 only, while #1 has an older Linksys WRT41G and a D-Link of similar vintage. They may only be capable of WPA (not WPA2). I also tried the T41 on a live Linux Mint flash drive and it wouldn't connect on wireless. Tried the X31 but for some reason it would not see the flash drive to boot on either usb port.
Have a few more variations I can try: an Intel 2195 A/B/G card (takes the same driver as the 2200 B/G I think), and one or two more Broadcom cards. May take several weeks to test those out. Today's results do reverse my previous opinions of Broadcom vs Intel, however.
The really bad news: the sound man claimed the wireless on the laptop had made the wireless mic system crash. I'm assuming the many smartphones around, a couple of which knew the logon, may have been on wireless N, though I don't know which of the two frequencies they would be on.