Idk if this happens with the GP or not, but I had this issue once with my monte... a wire behind the ignition cylinder had come loose... I think it was related to the chip in the key or something. I don't remember exactly what the wire was... luckily, a cousin of mine worked for GM for years and knew what it was. 2 starters later, both changed in sub-0 degree weather in a Chicago winter, and my problem was solved by installing a new lock cylinder.