Ubuntu 12.10 no network and no graphics
sudo apt-get remove bcmwl-kernel-source
sudo apt-get purge bcmwl-kernel-source
sudo apt-get install linux-firmware-nonfree
As I found, following these instructions and giving the machine a restart fixes the wireless adapter. DON'T go installing the Broadcom proprietary drivers through System Settings, Additional Drivers, or you'll just reset the whole lot back to the non-working ones!