After I play any of the games for a while, my monitor says "Monitor going to sleep", the sound starts skipping, and then I can't do anything. To get it back, I have to restart my computer. The problem isn't with my drivers, since I updated them right before and after the games were installed. So, any ideas TFS?

Check out your Power Options in the Control Panel. It's possible you've got some sort of power saving feature that's turning off your screen.

Well, I tried that, and it played for a little while longer, before doing the exact same thing.

UPDATE: I fixed TF2, but the other games still do the same thing.