The reason is that you don't have right drivers for the chip to work. I also have the same Broadcom device on my laptop and take my word, it is the worst network device out there.
The reason behind that is, first, it is a combined chip for both Bluetooth and Wireless LAN. Second, the driver. I have wasted a lot of time finding drivers for Ubuntu.
If it's any help, you can install drivers in Ubuntu by this command-
sudo apt-get install bcmwl-kernel-source
(First you have to update the repository by apt-get update
.)
Ubuntu is also a Debian based OS, so the binaries should be compatible (I am not completely sure). You can test this package in Debian. Maybe the trick will work.