Power off monitor will eventually reboot system

I get Windows 7 rebooting on its own under the following condition:

I power off the monitor and sometime later when I power it back on, I see that I am at the logon screen.
If I never power off the monitor, Windows does not reboot on its own.

I did change the power supply. sfc finds nothing. There are no new video drivers. My screen saver is set to 15 minutes (using the black screen) and the power saver option turns off the monitor after 60 minutes. All of this works as advertised without problems until I power the monitor off physically.

The error log just reports that an unexpected shutdown has occurred. I am using a new UPS which is working well.

Should I replace the video card?

MSI Radeon4550 amd Samsung PX2370

Cool. You sure it isn't just logging off?
Logging off does not cause a "unexpected shutdown" in the logs, I know.
I suspect it BSODs and reboots.

Try following this tutorial and post the result here.

It now bsod with code 7A occasionally. We will be changing the mother board or a capacitor on the mother board shortly.