Mobos and cases both have a circuit fault that will shut off the system during a direct short or power outage. Often with mine when the power goes out you cannot restart the comp once the power comes on. The green light flashes and you must turn off the black power switch on the power supply to reset the circuit breaker. Most power supplies support this and most cases also support this as well.
But just waiting should not cause the system to work. This sounds suspicously like something is overheating, cooling down and then working. When you boot the heat begins to build and the component fails....probably causing the blue screen in Windows. The problem is probably not Windows itself, but the problem is causing Windows to fail. Remember the whole thing is a system and works together. One failure can cause many other failures just like on a car leading you to correct the wrong thing. Be very careful in your diagnosis.
Best bet is to take everything off the board not necessary for booting. Unplug extra hard drives, floppies, CD-ROMS, sound card, LAN cards, etc., etc. Get your system down to just the boot drive, video card, CPU, and RAM. If you are using multiple sticks of RAM take the extra sticks out.
1. Boot the system with one of the RAM sticks. If same thing, wait, swap sticks, and boot again. Repeat until problem stops. If problem does not stop....it is not being cause by your RAM and all your sticks are good. Leave the system on for some time before rebooting and swapping sticks. We are trying to see if we can get the component to heat up, fail, and reboot the system. Also you may want to try using NO ram at all. If it fails and reboots, it's not your RAM overheating...it's another component.
2. Remove the video card from the board and and boot. You should get beep codes. Leave system on for awhile. There will be no picture but what you are looking for is if the system still shuts down automatically. If the component in question heats up again...it should theoretically cause the system to shut down no matter what task it is doing at the time - whether booting into Windows or sitting there telling you to put a video card in the mobo dummy. :)
3. If system does not fail or reboot itself.....then it is probably not a heat issue in the CPU, power supply, or board. If it was then the computer just being on should cause the component to overheat.
Basically what you want to do is try all different permutations and hardware configs to try to isolate the component that is causing the failure. Once you have ensure certain components are ok....include them in your next test because you know they are good. For instance, if you know the hard drive and video card and RAM are ok then try putting in the sound card and reboot. If problem happens....it is your sound card. If not, it is something else.
This method will show you exactly what is wrong. If it is your CPU...all of the above tests should fail eventually because there is always voltage going to the CPU. As the CPU heats up it should cause the item in question to heat up and cause the problem. If not it might be your chipset...although I doubt it because they can run just fine with no cooling fans and dont get nearly as hot as the CPU.
Also if you can get your hands on a DOS boot disk try to boot into DOS mode and just let it sit there at the command prompt. If DOS works fine...then it is most certainly something in the Windows boot process causing the problem. The only thing that will cause the computer to reboot in protected mode or real mode or any mode is a triple fault in the CPU. This can be caused by any multitude of code problems, errors, exceptions, etc. If you do not have a boot disk I have a diagnostic boot disk that I wrote that will simply boot and hang. But it does allow you to test the floppy drive, RAM, power supply, video card, etc. It's just a simple 512 byte boot sector floppy but it will show you that the CPU and everything are in working order if it boots. This is extremely useful as it is very hard to diagnose Window boots problems because so much crapola is going on.
You can try safe mode with command prompt, etc. Also you may want to boot with your Windows XP CD and let the computer sit there. If it does not crash....your hardware is fine. Choose to use the Recovery Console and then at the prompt type:
This is much more thorough than chkdsk /f or anything available in Windows. This will fix and correct any and all errors on the drive.....but it does take quite some time. If this does not fix the problem when you boot from the hard drive....reboot with XP cd and choose to repair the Windows XP installation. (choose Install, then choose repair, then select which installation of XP to repair). If this does not work when you boot from the drive, then I recommend completely wiping the drive - format (use FAT32 if you can - NTFS has major issues....directly from MS tech support). NTFS will no longer be supported once HPFS comes out. I've had NTFS.SYS get corrupted on boots, and then magically begin to work again and other weird stuff. NTFS sucks - the only person it prevents from accessing the drive is ...well....you. Everyone else can hack the stupid thing. NTFS can allow programs to put directories on your drive that you cannot get rid of, display the contents of, or erase.
This is pretty much everything I would try if I were to come to your house and fix the thing. Of course I'd also charge you $60/hour, but that's another story.