Just a few thoughts before you buy a replacement Logic Board; Wouldn't it be a cheaper step to test out a low-end GPU like a Radeon 9600 or GeForce FX5200 before gutting it out and replacing the logic board? It's a major operation in a G5 and much more involved that any other tower Mac or PC.
Even if it's not the graphics card after trying a known working one, at least you wouldn't have invested the hours involved in the logic board replacement blindly. And if it turns out that it is in fact the logic board and not the GPU, then the GPU resell value will certainly hold. (plus shipping costs will be lower due to being a smaller/lighter item).
Even if it's not the graphics card after trying a known working one, at least you wouldn't have invested the hours involved in the logic board replacement blindly. And if it turns out that it is in fact the logic board and not the GPU, then the GPU resell value will certainly hold. (plus shipping costs will be lower due to being a smaller/lighter item).