You need to connect to internet using some other adapter and run in terminal
sudo apt-get purge bcmwl-kernel-source
sudo apt-get install firmware-b43-installer
and reboot.
If you do not have any other internet connection, then download these files.
http://mirrors.kernel.org/ubuntu/pool/main/b/b43-fwcutter/b43-fwcutter_018-2_amd64.deb
http://www.lwfinger.com/b43-firmware/broadcom-wl-5.100.138.tar.bz2
Copy them to your home folder and run in terminal
sudo apt-get purge bcmwl-kernel-source
sudo dpkg -i b43*.deb
tar xfvj broadcom-wl-5.100.138.tar.bz2
sudo b43-fwcutter -w /lib/firmware broadcom-wl-5.100.138/linux/wl_apsta.o
For 32-bit systems download http://mirrors.kernel.org/ubuntu/pool/main/b/b43-fwcutter/b43-fwcutter_018-2_i386.deb
instead of the 64-bit package.
lspci -nnk | grep Network -A2
command output. – P.-H. Lin Aug 03 '15 at 03:01