Whoa, a computer like that belongs in a junk yard or something I didn't know computers that slow still existed :P. I'm just picking.. but I don't know any FPS or any Gun Game in general that would play on a computer that ... slow.
This is what I would suggest if you ever had the money to spare,
http://www.tigerdirect.com Go with an AMD Sempron, the slowest is a 1.6 2800+ at $90. If you get a Mother Board with onboard graphics and around 512Ram or 1024 then all you would need is Processor, MoBo, and Ram.. you could use your old case, monitor, hard drive, and all. I could price you parts and get you the best for your money which means I could probably price CPU, MoBo, and Ram around $200 or so. My CPU/Mobo costed me about $140. I can run mostly anything and never have any Lag problems, so it's up to you. If you can't spare money I would seriously stick with PS2 because as far as FPS or any other Gun Game you will end up playing alone anyway since most of those games don't offer any type of Multiplay.
If you don't have a PS2, I feel sorry.