1991 Jeep Cherokee no start cold weather

Engine will turn over but no start. Temps of around zero or below. When key is turned on fuel pump will not cycle. Also check engine light wiil not bulb test. If jeep is brought inside for a very short time key left on within 5 minutes you will hear fuel pump relay click and cycle pump. Then it will start. Sometimes the maintanance required light will flicker prior to check engine light coming on and the vehicle starting. The engine has died a few times at startup after letting off of key but once its running it has never died going down the road yet. We have replaced ground connections at engine and ignition switch still same.