Simple first - try removing the power and battery. Press the power button for 3 seconds (shouldn't do anything). Then replace the battery and power. If it starts up, you're good! If not...
Try removing the RAM (under the keyboard), and see if it gives you three beeps on startup. If so, try starting with only one stick of RAM, may just be failing due to RAM that's no longer any good.
If you don't hear three beeps (or anything) on startup with/without the RAM... probably a bad logic board.