I guess i should start asking for links for hows to and where to buys...
That's a hard one to diagnose. You don't know if it's the PS, a bad CPU, or a bad logic board shutting it down. Since it will boot it seems odd that it would be the PS, unless something is bad in the PS causing it to overheat shortly after powering up. Does it seem to run a little longer if it has cooled for a couple of hours as opposed to trying multiple boots.
One suggestion since you're hitting with a hammer is to disconnect the HD so it doesn't have a chance to get corrupted. It won't go to a log in screen of course, it will sit and flash the folder question mark symbol until it shuts down.
Did you try removing the CPUs and reseating all connections. Could be a bad connection. If you need instructions on it let me know.
Did you mean model A1117? It sounds like a late 2005. What speed is the CPU?
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