a problem from a few years ago.
The problem, believe it or not, can be caused by a defective battery. The one that keeps all the settings and stuff stored in PRAM from fading away.
Because the video card needed a certain push to get it started, and the dead battery failed to charge the capacitor that provided it, the machine would not boot. No video = No Boot.

Try removing the battery for 20 mins, at least, put it back in and try again. Replace the battery if necessary. It may not be the answer but it is worth a try


P