Soldato
Had some weird stuff going on with my P3 where pressing the on button just once would trigger the camera app to open, then it would constantly bring up the off/reboot/screenshot menu; despite turning the phone off completely it would then still reboot. Seems sporadic but I'm considering taking it back to CPW for a second exchange.
The camera and the off/reboot menu are all triggered by the power button. Have you checked and cleaned that area ... Bit of belly button fluff under the case ?