well, since you have stripped down the system almost entirely i can only recommend trying a different power supply.. i know for sure they could possible cause happenings like that.. the mobo might not be getting enough voltage, or too much, and responding in such a way that it protects itself by shutting down.
If you can get your hands on a differnt PSU, chuck that thing in there and try it. (preferably a good quality 300W or more) my only suggestion on a gutted system.. if it was memory you'd probably get blue screens or rebooting, but not shutting down.. you can try another stick of RAM too, but that's likely not the problem.. and it's also possible that it could be the CPU.. while VERY rarely, i have heard of defective CPU's which still run. (albeit not well) the only other logical option would be the case having to do with grounding the mobo i'd think.. that MIGHT also cause this problem.. i however would do the PSU swap first. the only option after that would be to get an RMA on the mobo if nothing else fixes the problem. Hopefully you have some spare parts.. they are definitely good in troubleshooting unobvious problems like this. Hope some of this jibber jabber helps...