Well, this is a last ditch attempt before I take the card back to the store. The guys on IRC were stumped to say the least.
Recently, I purchased an nVidia 6600GT to replace the GeForce 4 that died. Unfortunately, I'm having problems with this card. During startup, before it gets to the Windows login screen, the screen will switch off, as if it were going into sleep mode. This behaviour also occurs when loading maps and when loading HL2 (not the game, just the menu). Here's the clincher though: this behaviour is totally random!
Sometimes I'll get straight into Windows unscathed and be able to load HL2 and play for hours and hours, with full shaders and effects. At other times, I don't even get to login. This eliminates a possible overheating issue - a graphics card wouldn't overheat during startup or before any 3D graphics are loaded. There are also absolutely no artifacts on the screen as would happen if it were overheating (thanks m0p).
I met all the minimum system requirements for the graphics card. I'm running the latest drivers, and I've even formatted to no avail. There are no strange programs running at startup. I tried increasing the AGP aperture size via the BIOS from 64 to 128 which seemed to fix the issue. Unfortunately, loading a map in Hammer an hour ago caused the problem to show itself again. My guess is that there is a problem with the card itself - the GeForce 2 that I replaced the GeForce 4 with temporarily worked fine. Have I missed something? I really want to map!