I got the PM and decided to answer you here. Some ideas:
1) You said that you reset the Power Management Unit; but did you reset the NVRAM:
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As a diagnostic procedure you could also leave it turned on in Open Firmware mode and see whether it shuts down there as well; if it didn't it could be some sort of Operating System glitch.
2) You could also try updating your Open Firmware:
http://docs.info.apple.com/article.html?artnum=120068This might replace some corrupt information in the Open Firmware!
3) It could be a thermal shutdown problem either in the power supply or the motherboard. I think you can run that thing with the side open and if you do that and run a household fan full speed into the open box would it make any difference in the time before it shuts down? If it were to make a difference you might want to sell that power supply back to the people that you bought it from; it's unlikely to be the motherboard because you've had it all along.