Booting shuts down unexpectedly

I am having problems with my desktop computer with Windows 7 32-bit home deluxe booting. I try to power it up and everything goes okay for a while. Eventually the windows logo comes up, but then the computer shuts down without warning. Once this happens, the computer seems mostly unresponsive to a restart using the power button. Press power on does something (some lights come on), but it doesn't even get to the Bios. I have to turn off the power supply then turn it back on. Then when I press power on, the computer tries to boot up again. A couple of days ago when this first happened, upon reboot Windows entered a "startup repair" process. After this, the computer was able to boot. However, trying to boot today is even worse. While Windows is running the startup repair and tries to boot, the computer does the shut down thing again.

I'm not sure if it's a heat issue, as I've tried to boot from room temperature. Mind you, I don't know how long it takes for things to heat up, maybe 30s is all that is needed?

What really confuses me is that I have to cycle the power supply in order to boot again. Maybe there is a simple explanation for that though.

During the startup repair I'm given the option to do a restore, so I'll try that next.

thanks

Thanks.
I should mention that once booted, I have never had the PC unexpectdly shut down. Does that still make sense with the power supply being at fault when booting?

I was pretty careful when I spec'd out the power supply so it is fine in terms of size. I guess I'll pull some PCI cards and try booting to see if that helps. Maybe one of the cards is causing problems.

Would the CMOS battery have any effect on this?

Thanks again.
I ran ubuntu live of a CD and that worked ok. I also ran Acronis True Image to restore the c: drive. The restore went okay, it ran for an hour or so. When the computer rebooted into Windows, it shut down again.

I don't mean to disregard the power supply suggestions. Simply, I don't have a spare PS to test with and I don't want to shell out $100 if it's not needed.

Hi Smish,
I have a pc with exactly the same problem...
I've already replaced everything (Power Supply, Ram, Harddisk...) but the problem remains...
Did you solve the problem?