Game freezing up computer and rebooting

Recently (past couple weeks), I've been getting a lot of game freezes, which the result in a computer reboot within about 10 seconds.

I've received this in four different scenarios:

1. After logging in, when I select the top server in my list (Freedom). I get to this point by using the NCSoft Launcher (which remains visible after launching), I click or tab to COH, then I fill in my password (username is already populated). I accept the agreement, and then click on the server and freeze/reboot.

2. When selecting a player, right-click O (for Info).

3. When trying to place something in a base. I double-clicked to a room in Edit mode, then selected Place Item.

4. Logging back in after the reboot from trying to place something in base.

What's weird about all these situations is that my computer completely freezes, then reboots.

I suspect a video driver issue. I have an ATI Radeon HD 4200. I updated the drivers yesterday, but still crashing (although today it was only 3 and 4 type crashes, not 1 or 2).

I can provide information, just let me know what might be helpful. Thanks!

Let me add a few things before I provide any technical information.

This is a relatively new desktop, pretty low-end, around $500.
I run in Windowed mode, but not full screen.
Sometimes I have other apps in the background, like a browser.
I tend to have Contacts up, as well as several other windows (which are detached and placed around the screen).