2000 GMC 1500 electrical problem

When truck is running in park for approx 3 min the low fuel light comes on and guage goes to empty put it in park and returns to normal. Also if truck sits outside at -30 turn key and no click just dead. Changed starter and battery is good still same problem. Any ideas?

if you check tsb's for 2000 chevy, gm has a sevice bulletin out for the no start in cold weather, might have something to do with other problem