It is quite difficult to diagnose a problem when the requested data is not forthcoming. (Please read the long advice in my sig then reread post #2.)
To tell me what kind of card you have, please report the entry in the pci list you get with the lspci command. Please open a terminal and type "lspci" (without quotes), press enter, then look through the result for mention of your wireless card. Copy that, and paste it to the forum.
From the above, I am guessing you have a broadcom based card... and I am hoping it is pci or pcmcia and not a usb dongle or somesuch.
To give me a look at the output of iwconfig, please open a terminal and type "iwconfig" (without quotes) then press enter. Copy the result and paste it to the forum.
Have you read the article in the link? (Post #2)
Your reference to the card/driver showing up in the boot messages suggests you should look through your syslog for entries pertaining to your card. Especially after attempts to configure it. Open a terminal and type in "dmesg" (without quotes), press enter, and hunt through the result for mention of your card. The result from lspci will be particularly helpful with this. Please copy and paste anything that actually mentions your card, wifi, driver and so forth to the forum.
Note: you may get a more usable result with "dmesg | more".
That you are using bcm43xx driver is useful, provided
this is the right driver for your card. If your card is broadcom 4300 - 4399, then...
Have a look at the output of lsmod, to make sure that the bcm43xx driver is actually loaded. Sounds like it was loaded on boot, but it may have been unloaded for some reason. Or maybe sounds can be deceiving...
Even if the driver is loaded, you still have to install the firmware. That means you probably need to get a program called fwcutter and the wl_apsta.o file. Have a look at: http://hangdog.pihl.no-ip.org/index....d=18&Itemid=32
After the firmware is installed, you need to reload the driver.
# modprobe -r bcm43xx
# modprobe bcm43xx
After that you'd probably want to edit /etc/rc.d/rc.wireless.conf to setup your WEP key and SSID et cetera.