I own a 2006 Pontiac g6 GTP and as of a couple of days ago the battery had died from the recent cold. I jumped the battery and realized that the car still wouldn’t crank. I purchased a new battery and made sure it was charged and there was still no crank. The next day I got up early and started the car no problem and ran it and let it sit for a couple of hours and then it wouldn’t crank again. I took starter out to get tested and it tested fine and now when I go to start car it only cranks for maybe a second then dies out as if power is being cut. However for the past three mornings only the car will start and run fine but once I try again a couple hours later it doesn’t. Another weird thing is car will only crank for a second if my headlights are on if they are off car doesn’t crank at all. Can this be a faulty ignition switch?