Does the green sleep light stay on, too? If so, try resetting the PRAM a few times. A more thorough reset would be to take the battery out, disconnect the power adapter, press and hold the reset button on the back of the computer for at least 30 seconds, then plug the power adapter back in and try turning it on (if it doesn't come on automatically). That sometimes works.
If it still doesn't work (and you've ruled out things such as unseated RAM cards, bad power adapters, etc), then there's a chance you've got a dead power board.