Time to send it to the service center.
My N85 did the same thing. I got it to turn on after pulling the battery and leaving it out, then putting it back in and leaving it alone. After a random amount of time, pressing the power switch would switch it on, but the time and date would set back to the time it went off.
It did this for a while before I got fed up and returned it to Nokia service.
This affects almost all N series phones and is an issue with either the motherboard or firmware. They tried restoring the earlier FW version but that didn't do it, the phone kept misbehaving. Peeps having their motherboard changed are also having limited success. It's probably a design issue of some kind.
