Although an old question (I'm new here) I had a problem like this come into our shop about 6 months ago.

It was not a malware/virus etc problem. Wasn't a PSU issue either. And the motherboard tested fine using a P.O.S.T. card and booting from an offline OS.

Add to that it would only go through repeated reboot after the unit had been running a while (10-20 minutes). Then the nightmare would occur.

Letting it sit a few hours it would start up fine and stay running for a while. (see above)

Turned out (after much head scratching) it was the power button on the front of the unit. The contacts were wore out. Once the unit warmed up it would cause the contacts to separate enough to cut power. Then in a matter of seconds they would cool enough to power back on. A few second later the boot/reboot fiasco would start all over again.

What I learned in the process was never overlook the most simple of things while assuming it may be something complex.

Replaced the switch (cost me $.49) and the customer was more than delighted to dish out $40 for the repair.