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.
Ok, I just did that, we'll see...
I am thinking at this point that the power supply may be at fault, again... When I put in the new front panel switch, it started right up, and then began to shut itself off again randomly. The difference is that before I put in the new switch, I didn't get a power deflection (you know, how the lights dim a bit when you plug it in... I have a desk lamp on the same circuit... as soon as you plug in a computer you see a voltage deflection). As soon as I plugged in the MDD with the new switch in it, I got that for the first time since I had plugged it in after the power supply was repaired.
Now this afternoon, about 45 minutes ago, it died again, and this time, no power deflection plugging it in until I came out just now and started it up again. The first time I started, it went through the boot process, and then immediately shut down. I booted again, and now I'm up and running until it shuts itself off again. I think there is something not soldered correctly in the power supply repair, honest to God...
Jane, I wish I'd bought Applecare...