I have a Sapphire 2600 Pro and my computer seems to have problems on specific games, mostly on Source/Steam games. When I'm playing Counter-Strike Source or The Ship for about 5 minutes, my computer will freeze or reboot. Sometimes it happens as soon as I click to start a game and my videocard swtiches to 3D mode. And in the game Viva Pinata, my computer always reboots when I click to exit to desktop.
What's unusual is that I've been playing Call of Duty 4 and Conflict Denied Ops flawlessly with no reboots or problems. That surprises me because it seems that those games are more taxing on the videocard than other games.
It's worth noting that the freezing/rebooting that happens in The Ship is quite distinctive: Some of objects (such as chairs) flicker black a few moments before the crash, and some of the text can become garbled.
The first thing I thought was that it was a problem with my power supply. I thought it would be because I'm using a 20-pin PSU on a 24-pin motherboard, so I bought one of those 20-pin to 24-pin converters but there has been no change. My voltages seem to be okay. Although buying a brand new PSU looks like a quick and easy fix, I still have my doubts on if it's the exact cause of my problems. What are your opinions, folks from Legit Reviews?

Thanks,
Mark