had something like this on new 770, after the device was powered off it could be sometimes woken up only by connecting the charger, power key didn't work.

what helped for me is switching device to r&d mode. in this mode the device powered on reliably and only shorter press was needed. then after few days i also tried to disable r&d mode and the problem didn't come back. power on is now reliable even if r&d mode is not enabled.