The STA driver will not work with your broadcom chip and, in fact, must be blacklisted so that it doesn't capture the system resources needed by b43legacy. The BCM4306 chip is frankly a royal pain in the neck. I have a couple of old laptops that use this chip and must go through the same-old-same-old for every install. To do the following, you must be connected by ethernet cable. These steps will not work without a wired connection. These steps must be done in order and to completion. Skipping any step will gum up the works and require that you start over from the beginning.
1. bring up "additional drivers" and disable the sta driver. Your b43 legacy driver cannot be installed that way.
echo "blacklist sta" | sudo tee -a /etc/modprobe.d/blacklist.conf
These two steps will blacklist competing incompatible drivers.
echo "blacklist wl" | sudo tee -a /etc/modprobe.d/blacklist.conf
4. Then open synaptic package manager and search for bcm. Mark every already checkmarked box and tag for removal. Apply.
7. The output will consist of one or two network cards, depending on whether your wired ethernet card is also a broadcom. We are not interested in the wired card. Look instead for the reference that contains BCM4306. The important number in this reference are the four digits immediately following "14ef:" If they are any of:
lspci -vvnn | grep 14e4
then we must install b43legacy. If they are anything else, then we must install b43 (not legacy).
8. Run synaptic again. Search using bcm. Check the box "b43-fwcutter" for installation. Then, based on the results from step #7, check either firmware-b43-installer or firmware-b43legacy-installer for installation. Do not check both. You must choose one or the other based on the results from step #7.
10. To check, do:
This should return a nubmer of lines showing the b43 and variants are now residing as kernel modules.
11. To check that sta and wl are no longer gumming up the works, do:
This should return nothing. Your wireless should now be working. If not post back to this forum and we will try more troubleshooting.
lsmod | grep -w sta | grep -w wl