Hah!!!!! Found it!!!!

I'm a very happy boy right now.

Okay, one of the reasons I'd chosen to install 2000 Server on this box was because there are times when I want to remote-control it using Terminal Services.

Turns out, that's precisely what those games didn't like. Well, more specifically, it's what the Nvidia driver in combination with those games didn't like. Deinstalling terminal services solved the problem. Those games now run better than they ever did with these newset Nvidia drivers.

So y'all can take your Fischer-Price OS and... well... go play with it or something.