In case anyone else is still having this problem, I figured I'd tell about how I finally got it working, sort of.
It turns out that it mostly works, but not entirely. I disabled WEP on my AP, and lo and behold, it works. This, of course, creates a security problem, but I solved that by enabling MAC filtering on my AP. Now, it works just fine, and hopefully, the Open Source Broadcom Linux driver at
http://bcm43xx.berlios.de/ will have a stable release soon (I think they've got WEP working), and I won't have to use proprietary Windows drivers anymore.