Ok, I found this possible solution on the Knoppix STD forum. I'll have to give it a try and let you know for sure.
I had the same problem, but fortunately knoppix includes the sources for the kernel, and the standard tools for Makefile's. So you can download the drivers source from
http://www.broadcom.com/support/etherne … rivers.php
store them in a floppy or USB drive, start K-STD, unpack, and write 'make' in the src directory. Note that 'make install' will fail because /lib/modules is read-only, but you can 'insmod bcm4400.o' anyway, and then menu-> internet-> connect-> netcard config will work.
I think this should work for any unsupported hardware, despite some comments in other posts suggesting that issues with unsupported hardware can only be solved by doing hard disk install.