[Question] What's a good single-player FPS game?

I second System Shock 2 and Deus Ex. They have more adventure/RPG mechanics to them than just shooting, but they're still excellent games. Half-life and Half-life 2 probably have some of the better single-player campaigns out there, so those should be your first stop I think. F.E.A.R. is another one to look for when you eventually upgrade your videocard.

Also, your videocard will actually run Doom 3. I'm not sure why it says it won't run it, granted it won't be the smoothest, but I played it on a Geforce 3 and it was quite playable on low settings. Other Doom 3 engine games like Prey and Quake 4 are a bit more questionable, they push the engine quite a bit farther and it would likely get much more choppy in places. You can get a pretty decent videocard for around $100 though, sure it's not top of the line, but it would be able to play pretty much any current game at medium-high settings. The rest of your system is up to speed, so you'd see a big improvement since it's your videocard that's holding you back at this point.

Jam it back in, in the dark.