I'd check to make sure the motherboard is not making any contact with the case except on the standing poles. If you are sure that nothing is causing it to short out, then unplug as much as you can (ie CD, HDD, expansion cards) If it then starts properly then add in one device at a time. if it starts dying again remove the last device added and try another. Everything else works? then you've found the problem. Every drive/card you add after a certain point causes the shutdown? then your powersupply can't handle the load.
Hopefully this will help you locate the problem.
If however you still have problems running on the bare minimum (board, CPU, RAM, VID Card) then the problem is either the board or Power Supply. I'd recommend changing the power suply first since they are fairly cheep.