Hello lukadam. Welcome to the Forum.
I trust your wired connection is working at the moment because it will make this easier.
Open a terminal (Ctrl+Alt+T is the quick way), and run the following commands
Click on the Network icon, any networks showing? If yes choose yours enter the password. If no post back here with the the terminal output from the commands copied and pasted into [code] brackets. Click on the # symbol and paste between the [code] [code]. This will preserve the formatting and make it easier to read.
sudo apt-get remove --purge bcmwl-kernel-source
sudo apt-get install linux-firmware-nonfree
sudo modprobe b43