Grim Fandango refuses to do a damn thing when I click on the .exe file. Graphics card is AI Mobility Radeon 5730. No idea if it supports whatever; don't even know how to find out. Anyone else having trouble, though?

According to this: http://www.techpowerup.com/gpudb/1649/mobility-radeon-hd-5730.html the ATI Mobility Radeon HD 5730 *should* support OpenGL 4.3, which is more than enough to start the game after the OpenGL 3.3 check.

I would recommend updating your GPU drivers, or even uninstalling and reinstalling them, if updating them doesn't seem to work.