This tutorial is applicable to LinuxMint Debian Edition for it doesn’t come with the Hardware Driver option (System->Administration->Hardware Drivers) found in Ubuntu and LinuxMint. Installing LMDE will not automatically install the driver for you so you have to manually do it from the Terminal.
Steps are outlined below:
You are required to connect to the Internet with the LAN interface before proceeding.
1.) After successfully installing LMDE, you have to update it first prior to installing the driver.
sudo apt-get update && sudo apt-get upgrade
2.) After a successful update, we can now install the desired driver for our Broadcom wireless card:
sudo apt-get install b43-fwcutter firmware-b43-installer
All you have to do is wait for the installation to finish and you will be able to use the Broadcom wifi card after a restart.
This was one of the easiest fix I’ve ever encountered on a linux machine.