In terms of the using any machine to be a Lindbergh, I think if you had basically the same PCI cards in a normal PC it would possibly run. I'm not sure quite how the PIC chip communicates with the motherboard though, possibly over parallel port, so it's probably a big job to setup another computer to run like a Lindbergh? Lindbergh games can be run on a normal PC anyway now.
In terms of the different video cards, depends what multi you want to use - some will allow the use of different cards, others won't. I've found that all games will run on the 7800GS, so if you've got one of those then theres no need to upgrade really, if not maybe look for one of those cards online? If you're quite okay with working with Linux, you can find all the stuff for the multi which supports other cards for free out online. If not, I think you can probably still purchase one of the multi's from this forum, however I believe they require the original graphics cards to play.