The bcm4303 chip may not be fully supported with the native Linux driver.
b43 - Linux Wireless
Anyway, for it to work at all, you need firmware installed. If you take a look at the output of this command, it may actually tell you what is wrong.
Here are the instructions for installing the firmware.
b43 - Linux Wireless
To determine the firmware that you need, first find out which driver your system is using.
Look for either bcm43xx or b43, and then follow the instructions on the Linux Wireless page link above.
Now, if you find that it doesn't support your wireless, you can use NDISwrapper. This may be your best bet anyway. Just make sure that the native driver (bcm43xx or b43) is not loaded, and then you need to blacklist it to keep it from loading at boot. I'll help you on this when you need it.