Sounds like yours suffers from the common power jack issues. It may show signs of life if the jack is held in a certain way. If so, you'll need to disassemble the machine and grab a soldering iron to touch up the four or five pads around the surface-mounted power jack.

Initial power with a drained PRAM battery (or after the reset combo) will be a combination of the sleep light illuminating, the itty-bitty fan screaming, a pop from the speakers, and the hard drive may or may not spin up. After a second or two, everything will immediately quit. Then, a press of the power button, the machine should chime and everything ought to be hunky-dory.