I'm having an identical problem as the original poster. My Dell Mini 9 almost won't connect to specific wireless networks. Some of them it works fine, some of them it doesnt like for some reason. And the networks it DOESN'T like to work on have multiple wireless devices working flawlessly on that network, so it's not a router problem.
Each and every time I attempt to connect I get the yellow warning "limited or no connectivity". It's because the DHCP on the router is not assigning an IP address to the wireless card. As far as I can tell, it has something to do with the WPA encryption as I don't have a problem connecting to unsecured networks.
I have tried updating the firmware on my router, updating the drivers for the Wireless Card (this includes trying dells drivers as well as broadcom manufacturer drivers), resetting the internal wireless card and cleaning it's copper contacts, and even using the broadcom wireless utility to connect to networks(Interestingly, the Broadcom wireless application WON'T work, it tells me that the "internal configuration is incorrect". I checked the model number on the NIC card I have on the inside and it's the one that ships with Dell Mini 9's, so I don't know what to expect.)
I've ran a few live linux distros and each of them does NOT have a problem connecting, so it's specific to Windows XP with encrypted networks, atleast as far as I can tell.
Finally, I WAS able to get a temporary work around by manually assigning my wireless card an IP address in the network configuration settings. But even THAT stops working after a restart/a few hours. I've been in computer repair for 5 years and I've never seen a glitch like this avoid repair so thoroughly. I'm ready to just re-install Windows XP and/or rage quit.