as far as i know broadcom chipsets are well supported under linux. BUT i think they are binary only drivers (so they dont comply with ubuntus general "open source only in the main package repository's" rule.
Two things you should check:
1. Under "System"->Systemsetup(or what ever its called in the english version .... its the second submenu under System)->Hardware Drivers (or what ever its called in the english version ... look for something with drivers)
--> here you can activate closed-source drivers .... maybe you will find you wireless card here ..
2. if the first thing didnt work, try to activate the "universe" and "multiverse" repository's with synaptic (package management tool)
then search for broadcom .... maybe you will find you drivers ....
if nothing helped, aks on the ubuntu forums ... they can help!
With this world there is no understanding, we belong their only to the extent, as we rebel against it (Theodor W. Adorno) --> if somebody knows a "official" translation for the well known german quote ... pls let me know!