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As with any potential hardware fault, it is always best to strip the PC back to it's most basic setup. Remove one of those RAM sticks, then boot, then remove the other one and boot. Disconnect the optical drive and boot...you get the idea...
Check
every single cable and connection pay close attention to the "power and lights" header, making sure that all of the connectors are the right way 'round.
Check that every expansion card is seated properly.
Remove and replace the bios battery (with the power out).
(if you can) Test the parts..especially the Power Supply Unit in another PC