To begin with,airsnort doesn't support the broadcom chip.RTFM
To get your broadcom to work under linux,checkout ndiswrapper.It uses the windows drivers.Works like a charm,but when I built the driver on knoppix,I couldn't get it to load. (I have a compaq notebook with the same chip)
If you want to use airsnort,you'll need a prism2 based card,or a couple of others that support monitor mode.I use a dlink dwl-122 with the wlan-ng drivers.(prism2_usb)However,the version on knoppix doesn't support this card.The newest stable drivers do.Maybe in the next version.
Good luck,but be prepared for some reading if you want to get this to work.