I have had a similar problem. A few months ago I installed a 1080p 1080x1920 monitor. After a while it started shutting itself off. I reinstallled a 1200x1600 older monitor and that worked fine till a few days ago when it started shuttting itself off. I googled and read about the problem. I saw few solutions.
1. In windows 7 I had changed the power setting to lowest possible. I changed that back to balanced and monitor never turns off. No help.
2. I ran the free Scisoft Sandra and Wizard programs, both said I had 2gb ddr2 memory.
3. I tried another cable between monitor and computer, no help.
4. The capacitors (round black things) did not seem to bulge from sides or top on the mini motherboard.
5. I looked at the Coolermaster website, entered my computers components and they suggested a minimum 278 watt power supply. I removed the Chiefmax 630w 34a on one 12v rail power supply and installed a 600 watt Coolermaster 32a on one 12 volt rail power supply I had. No help.
6. I turned my HD 5750 video card memory settings to 80% using the AMD ATI driver. No help.
7. In bios (F8) I turned my memory setting for ddr2 from 666 to 500, limited help.
8. I turned off the computer, unplugged it from the wall and pressed the power button several times because there is a trickle charge even when off. Limited help.
9. I installed an older monitor 1024x1280 that used an older smaller cord adaptor on the monitor end. Now it works, if I game I can play a couple hours then the monitor turns off but it will restart and is useable. Without gaming the monitor seems to stay on.
Next I will try unplugging one stick of memory at a time and running the computer till monitor turns off. Then try using another wall plug because reducing power seemed to help. Last possibly replacing the $50 motherboard.
The hd5570 solved the problem, it works fine, uses half the power and lets me use the 24" Dell monitor I bought 4 months ago. I could not use the Dell monitor for the same reason, the monitor would turn off, so I installed an older 1200x1600 monitor I had and that worked till recent when the 1200x1600 monitor started turning off.
I think either the hd5750 was too much for my power supply or was bad. I think bad since I have had 3 other higher power video cards go out in the last 5 years. I average gaming more than 1 hour a day.