I hope I'm not asking the obvious...so please forgive me if I am.
If you are trying to use the power button on the back, have you tried using the one on the keyboard?
Alternatively, if you are using the button on the keyboard, have you tried either a different keyboard or the button on the back? If you're using a KB with a removable cord, are you sure the cord is fully plugged in and good(a readily available S-Video cable will work perfectly).
Either of these can be a point of failure, although a bad button on the computer is more common(admittedly not as common on this series).
Aside from that, the only cause of a completely dead computer I can think of is a power supply.