Don't know where you read about Broadcom Wi-Fi chipsets being most
compatible with Linux when quite the reverse is true - Broadcom are
the most difficult to get working in Linux, some of their ethernet
chipsets are a pain to get working too, never mind wireless !!

However, if you are using Ubuntu 10.04LTS or higher then connect to
the internet using an ethernet connection and then let the system
check for updates - it will detect and offer installation of drivers
for graphics / Wi-Fi etc along with regular updates, or you can go to
[ System / Administration / Hardware Drivers ] to force a check.

As for the antiquated Asus card, it may be too old to work at all but
the hardware driver check would be a good first step.