Crashing to desktop with an HL2 error can be caused by all kinds of things, but I can think of five likely culprits.
After trying Nemo's suggestion of disabling the game overlay UI, you might want to look at:
1. Out of date/corrupted drivers.
Go to the video card manufacturer's website and find the most recent drivers that match your video card. If the computer is a laptop or Dell, you will more than likely need to visit the manufacturer's site to get the appropriate drivers. Sound card and network card drivers are important to check, too.
2. Out of date/corrupted DirectX.
Give these a try:
[link=http://www.microsoft.com/downloads/details.aspx?familyid=2da43d38-db71-4c1b-bc6a-9b6652cd92a3&displaylang=en]For Windows XP[/link]
[link=http://www.gamesforwindows.com/en-US/AboutGFW/Pages/directx10-a.aspx]Windows Vista[/link]
3. Low computer specs unable to handle the game.
If the computer's a little old or on the cheap side, turn down some settings and see if that helps. Also, disable any background processes you don't need and close all other programs you don't need, especially Skype, web browsers, MSN, BitTorrent, Limewire, and the like. They're horrible on your CPU, RAM, and HD.
4. Interference from background processes.
See above, but you may need to do some additional work. Disable any virus scanners (after giving a good scan, just to make sure there aren't any virii adding to the problem) or hidden startup processes (if you know how to use msconfig), and use the task manager (Ctrl+Alt+Del) to kill anything you don't need.
5. Bad Steam/TF2 install.
Uninstall TF2 and delete its folders in your Steam directory, and reinstall. If that doesn't work, uninstall and reinstall steam.
