The problem here is that we're dealing with such old technology that it's difficult to determine where the fault is. I can't tell if it's a bad graphics card or if your motherboard is shot. About the only thing I could recommend is purchasing a new graphics card and hoping that it works. The problem with that, however, is that most cards that should work with your computer are no longer supported by their manufacturers.
The cheapest of the few exceptions to that is this HIS Radeon HD4350 AGP 4x/8x