DaRon had that issue on my P8...checked the IMEI, got a shipping label, sent it for repair, got it back within 10days or so.
Yeah, same with me. One might have to go through the reseller where one originally bought the phone, though, if one didn't buy it from Google, I don't know. The described issues sound a lot like a hardware problem. Note that highly likely they'll wipe the phone and return it back with the stock OS installed.