Pull the battery out, and leave it plugged in with mains power on for a couple of hours.

I've come across a few PB 1x0s like this that haven't been used for several years, seems to be an issue with the battery having too low a voltage to charge and "kick over" the Mac at startup. Once removed, and the PRAM battery charged for a little while, you can plug the battery back in.

If this fails, time to take her apart, and reseat the RAM and processor card.

JB