Welcome to the forums, the first step is to figure out which chipset you have:
Broadcom makes several different cards, and it's important to know which one you have before proceeding.
Alternately, you can boot with one of the distros that does work, and use:
to list the modules in use to see whether it's b43, wl, brcm80211, etc.
No matter which module you need, you will have to download the firmware (using a temporary wired connection).