I skimmed through the thread, and I didn't see anyone mention it, so:
Good Old Games
Since, it would seem, that you are more interested in a quality gaming experience than in graphical goodies (as it should be) check out GOG.com. They have many a gem from everything from old DOS games up to and including the brand new game
The Witcher 2. Witcher 2 is made by the sister company of the guys who run GOG.com (CD Projeckt RED and CD Projekt, respectively) and would not likely run on your system, just including it as a reference.
All of them are DRM-free. No copy protection, no BS. Everything is Digital download but requires no internet to install or use once downloaded. These guys are a class act, and I HIGHLY recommend them.
As for specific games to try? I've gotten a lot of hours of fun out of emulators for old Sega systems (yes I owned the original systems and games - that's part of the fun, bringing back memories)
You could try games like Descent I & II, with one of the engine rebuilds for true 3d and modern controls. Games like DOOM, Duke Nukem, the Fallout Series, Arkanum, BASS, HOM&M series, Ground Control series and perhaps even games as "new" as the original Far Cry and IL2 Sturmovik, Psychonauts, etc. <- most of those available from GOG. Really though, it's a matter of taste, so it's up to you to decide what you like