Once again I am casting a wary eye in the direction of the motherboard.
The A7V uses on of the earlier Via-based Athlon compatible chipsets, these are known for strange (and annoying) incompatiblities.
The GF3 Ti200 is an AGP2.0/4X card, the FX5600 is AGP3.0/8X and could be incompatible (ie, too demanding power-wise) with the A7V's AGP slot.

This kind of incompatibility is what forces users of Via-based motherboards to shut off fast writes and throttle back the AGP slot to 2X or even 1X to stabilize their system.
Slot A motherboards were horrible for this, first-generation Socket A were nearly as bad.
It may be that the GF FX5xxx series of video cards simply aren't backward-compatible enough for that type of motherboard (which, as I read this over, vindicates several of the posts above). I just didn't want to place sole blame for the problem on the video card. I spent about a year trying to upgrade a Via-based motherboard that simply wouldn't accept anything more than a certain outdated grade of card (very frustrating! ). Via chipsets are always twitchy at roll-out, best to get the 'B' revision after the bugs are worked out.
//rant off