Open a terminal and post the results of ifconfig, iwconfig, iwlist scan and lspci | grep wireless here... *It's supposed to be one command: "lspci | grep wireless" (the '|' sign is shift+backslash) - that should list all pci devices that have the string 'wireless' in their name and/or description.) I'm assuming your wifi card is a PCI one, and not a usb dongle. You can do a 'dmesg | grep wireless' too while you're at it.
Your wifi is reported as 0c:00.0 Network controller: Broadcom Corporation BCM4311 802.11b/g WLAN (rev 01) and it doesn't say that it'd be a firmware problem... Ubuntu should recognize it. If you have access to a wired connection, try System Settings -> Additional Drivers (in 11.10) to check if your card requires proprietary drivers. Another thing you might want to try is to search for the string 'broadcom' in the repos (in terminal do apt-cache search broadcom, or via Synaptic, that might be easier and see if any package matches your card and hasn't been installed).
Another idea is to check the BIOS and/or double check that it is not turned off - on the 620 there is an Fn+don't-know-which-button combination that turns wifi on and off (on the 610 sure was). Make sure it's turned on and not disabled in the BIOS.
I did some googling, and came up with some old info - if everything else fails, you can try using ndiswrapper. Here are two links for further info:
Ubuntu forums thread
Plase note, that both of these are old, and probably - and hopefully - there is a native driver for the card. I seem to remember running Ubuntu on a 620 without issues but I might be mixing it with something else.
Finally, here's a recent information:
You need the firmware-b43-installer package instead of the bcmwl-kernel-source that Ubuntu installs. Install the right one with sudo apt-get install firmware-b43-installer and remove the wrong one with sudo apt-get purge bcmwl-kernel-source (you can use 'remove' instead of 'purge', it's just my habit to purge stuff that I don't use any more). You'll need a working connection, so try to get a cable for your router.