Okay, so I did look around a bit before I started this thread, and I haven't seen anyone else with the same problem yet so I'm starting the thread.
I downloaded Trackmania, Audiosurf, Portal and Garry's Mod fine, and run them perfectly on my new HP laptop. I bought the laptop with Windows 7 on it, so it wasn't an upgraded computer (Just in case that might be a contributing factor).
But when I went to launch Counter Strike: Source and Half Life 2, it comes up with this:
I'm wondering if this is a problem with installation or downloading, or Windows 7 compatibility period.