It's probably the power supply. Do you get any diagnostic lights on the logic board?
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UPDATE 2/26/16
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The diagnostic LEDs should lit up when you press the power on button if the power supply is good.
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There is also a CUDA logic board reset button on the logic board. Press the CUDA button, ONCE! It is located to the rear of the battery housing. It looks like a small pencil eraser in a metal square..
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Have you replaced the 3.6V/850mAh 1/2 "AA" Lithium PRAM battery?