|Subject : Nats fault|
Missed the solution by ...thaaaaat much!
Take the keys out of the ignition and keep them in the house somewhere warm, just in case there is a crack in the printed circuit board in the keyfob???
(cold causes the board to shrink, opening up a gap, heat expands it..contact made again....)
Also could you disconnect the vehicle's battery overnight (this will force a reboot the ECM) (take the opportunity to give the battery a nice long charge at the same time) and try again in the morning.
After that you may need to scan for codes on the ECM