I managed to rescue an Optiplex 755 from my workplace under similar conditions... The plan was to turn it into a high-end Win XP machine. First thing I did was to replace the lowly Pentium Dual-Core E2160 with a much more capable Core 2 Duo E8500. This was a very easy and cheap upgrade, as the chips are dirt cheap on eBay. I also wanted a better video card, but my machine is the desktop model, so I'm limited to low-profile cards (I know there's a right-angle adapter for larger cards, but I don't have it)... ended up going with a Radeon R7 240. I was able to get this all working, but was getting lousy performance from the Radeon under XP. I couldn't even run Oblivion at a playable framerate, and I couldn't figure out what was going on.
Eventually I decided to try wiping the machine completely and installing Windows 7... and suddenly everything was running great. I can crank up all the graphical options on Oblivion and it runs smooth as silk. So I guess ATI's Windows XP drivers just totally suck balls when paired with newer cards? I don't know, but I've left it as a Win 7 machine. Stalker, Unreal Tournament, Ultra Street Fighter 4... they all run great. So yeah, moderate gaming is absolutely possible with these kinds of machines.
I definitely recommend swapping in a faster processor (Your boards might support Core 2 Quad, but you might get better performance using a Duo with a higher clock speed, as single-core speed tends to be more important with older stuff), but if you want to go with Win XP, I'd recommend getting a more period-appropriate card rather than something actually modern like most people have recommended here.
--Zero