Hi, I am having sort of a familiar problem as the original post. I have this car for almost 20 days know. It's an automatic 05 Cobalt sedan.
Three days after buying it, I put in a new battery of 1000 amps. Since two days ago when I start the car it acts like a dead battery, but the engine runs. I have a Voltage meter and it marks 12.27, 12.67, 12.0, (red light) and it's like crazy until it gets to 13.8, 14.1, 13.0, 12,8 etc. (after running it for 13 minutes or so).
I turn off the auto lights, and the voltage comes up a little higher. I don't know if it has the original alternator. I had a Montero and sold it because of this, I changed 3 alternators in one year. What can it be? New to this kind of car also.