Have you ever witnessed this machine powering on?
The problem is often that the cable that connects the power button to the board is disconnected, or needs to be re-seated, or that the entire power button/cable mechanism is defective and need to be replaced.
I'd take the topcase off (see the guides for instructions) and see if the power cable is plugged in. If it is, disconnect it, and try powering on (with the topcase loose -- there's no need to put it all the way back together for testing). If it powers on, you're all set. If not, disconnect the cable again, and use a pair of metal tweezers or a screwdriver to bridge the two pins in the socket that the power cable plugs into. This is effectively the same as pressing the power button. If it powers on, you need to replace the power button/sound electronics and cables in the topcase. It's all connected to the underside of the topcase by about 5 screws. You can also get a replacement topcase with the parts included, but make sure you get the specific one for the 1.33GHZ model 12" G4, because it's different than the previous topcases.
If it doesn't power on, it could be the board. I'd also remove the battery and RAM, just to see if that makes a difference. Sometimes the socket for the power cable breaks off of the board or is loose, in which case you're probably out of luck unless you're good at soldering.