Yeah, your GPU is causing this issue, you can shop around and see if you can pick up an old VGA card that supports Shader 2.0 (it allows pixel transparency or somthing along those lines thus games with transparent pixels in them can't / won't run) because I am assuming that on such an old system you don't have any PCI Express slots.
If there arnt any VGA cards with shader 2.0 support your only solution will be to replace the Motherboard to a more modern one, this would result in you needing to upgrade pretty much everything else ( bar the HDDs), so if I were you, I would either throw in the towel or get a new Case and build a system from scratch.