If there is no startup chime, I suspect bad capacitors. I have one like this too, sometimes it will work if I fiddle with it enough. I've had some superstitious luck by removing the pram battery and shorting the terminals in the battery holder for a few seconds. (That probably doesn't make a difference, but why not try I guess.)

If it's capacitor-related, you could try washing your logic board, that could probably help. Search this forum for some good info and tips on washing your logic board.