This leaves two options:
Disable onboard NICs in BIOS and/or insert a new card with known drivers
or
Try every driver ever issued, including, for Linux, those that appear to be branded by another foundry, recompiling where necessary.
Sometimes you can get lucky by finding a specific answer on some obscure Forum from someone who has actually succeeded with the specific system like yours - this is rare, though. Guessing is like trying to win the lottery.
Ah, well, I suppose it would be easier to use a Live CD distro that works. Guess it's ZenLive then, which is too bad because I prefer Puppy's features.