Why is my Neo3Do power button not working?

This is covered in some detail on the troubleshooting page.

If the device will not turn on when the power button is pressed, it usually means the device is not charged. This could come from a faulty charger or a bad battery.

If it's not either of those, it could be the motherboard in general that has a problem, or the power button specifically.

Regardless of the cause, all solutions require replacing the defective part.