It's no
t very likely that it is a hadware problem: If the box does a normal shutdown it's probably shutware related, or the poweroff buttun is faulty and make contact itself.
It won't be a thermal problem either; the box would then shutdown but not restart.
Set your CMOS so that hitting the poweroff button will only shutdown your box if it's pressed for 4 seconds (be aware, this means a powercut, no normal shutdown) and see if the problem still exists. If so, I'm pretty sure it's software related.
The PSU can't be at fault (at least not likely) since it can't give Winodws a shutdown command.
Edit: Typos!!!
should of course be