Generally, you need to install the "firmware" in order to use the B43 driver for Broadcom chipsets. (Which is what you have - a BCM 4306, just like the one in my laptop.) I don't have Ubuntu installed on my laptop, so I can't speak with any authority about Broadcom wireless setup for Ubuntu, but - IIRC - the Ubuntu LiveCD did work when I tried it on my laptop.
If that's true, it should have worked "out of the box" for you, so I guess wy recollection is not correct, eh?
Check to see if you have a program "b43-fwcutter" installed on your system. (I.e., start a terminal window and run the command whereis fw-cutter) If you do, run it and point it to the CD with the Broadcom wireless drivers on it. (That's the CD that came with your laptop. You may need to find the "wireless driver subdirectory" on it to locate the *.sys file you'll need, which will probably be called something like truemob.sys, but that's just a guess.) Use the command sudo fw-cutter to run it, and write the output to /lib/firmware. (You need "root" access to write to /lib - that's what the sudo prefix does for you.)
Before doing all that, you might want to check the "restricted" repositories to see if there might be a Brodcom 4306 driver there you could load.
Oh, another question: what security are you using on your wireless connection? If it's WPA or WPA2 you may also need to install the wpa_supplicant package.