Thanks. I had the same problem after a major update. I live in a Third World village in Mexico, and several poor kids come to my house to use the Internet. I have accumulated 4 machines plus a new HP 7 Plus tablet. They understand at my house they use Linux in English or they don't use my machines. Kids are clever!
I had an HP netbook with Broadcom wireless on it and as OP said, the update killed the wireless. I had used PCLOS in the past, but there were rumors it was shutting down. It didn't but I installed Bodhi. And, now it didn't work on wireless. I hate having to install a new distro.
I typed in the command you gave above, and it aborted, saying I had a low power BC4312 which is indeed true.
So, it said (or implied) to enter:
sudo apt-get install --reinstall firmware-b43-lpphy-installer
I did, and after reboot, I am also on the air.
I will be putting this in my large command file for future reference.
Note that when I looked at Synaptic to lock it, the only b43 was the cutter package.
Did I say thanks?