Hm. Debugging this is going to be difficult anyway since Dominions/Dominions II have a small fan base, so the probability of finding someone with a near-identical configuration might be low. You might still be able to find other assistance -- perhaps the nVidia newsgroup, forums like those at
www.ntcompatible.com, similar.
I've an ancient Frankenstein's Monster of a machine myself, and the one bugaboo I've sometimes run into is nVidia -- some drivers failed for Shogun, some drivers (again hit or miss) were buggy for Combat Mission, etc. My understanding is that the video card companies frequently cut corners or sacrifice complete compliance with APIs in order to eke out more FPS.