WAY too many possible issue's here. First and foremost, reinstall Half life and Steam. Then reinstall your video card and motherboard drivers. If you are still having problems then:
Step 1 Viruses
Scan your computer with several antivirus(trials, so you can dl for free) programs such as Adaware, Hijackthis, SpyBot, etc... Then do a regsistry tweak.
Step 2 Hardware failure
Go to download.com and get memtest. It's a small and very easy to use program. Use it to scan your memory for errors overnight. If you get so much as 1, then that is probably your issue.
Next, defrag your hard-drive. If it says you have errors in your clusters, think about getting a new hard drive.
Finally, get a 3dmark demo and run it a few times and see if you can't get it to crash the computer. Really, it would be best if you could run this all night to really stress the hardware out. The point here is to get either your CPU or video card to fail.
If everything I said to test here checks out, then it's most likely not a hardware problem.
Step 3 Driver / Software Issue
Reinstall all your drivers including your mobo's. Reinstall DirectX and make sure your up to date with them all, including your windows updates.
If you do all that then you have a **** good chance to fix the issue. If not, it's really out of your hands and you should take it to someone who knows what they are doing and can run further tests. You could also reformat and reload the OS, that will fix any software issue... and if you still have the problem (make sure HL2 is one of the first things you install other than updates and drivers, so you know there aren't any software conflicts) then you know it's a hardware problem. I have a feeling you don't want to go quite that far with a little error like that
Good Luck