You could have the battery load tested, but usually if the car won't even start with a jump then it's either a bad connection or the starter. Check all the connections, try a ol' hillbilly trick take a hammer and tap (tap not whack) the back end of the starter. Does your Cobalt have a V6? Every Chevy with the V6 that I've ever owned had problems with the starter, had a Chevy with the 305 V8 never had to replace the starter

I would check all your electrical connections. When I had this problem, i thought I had to start switching things but it turned out that the starter's positive and negatives came a little loose and touched, causing a short. Just check all connections and clean the terminals and wires with a wire brush.

If this doesn't work, you will need a new starter. If it clicks, the relay is getting power. But this happens a lot to vehicles that haven't had their starter nuts tightened enough and the cable sags down over time and touches another cable, causing short circuit.

You hit the nail on the head. Obviously when a "jump" from another car starts the engine your have a dead battery. To prove this to yourself, take the 12 volt battery to any store that sells new ones *other than Auto Zone and ask for a free 15 second battery load test which will tell you the reserve amperage capacity. Amperage spins starter motors not voltage.

It's the battery, or bad connections on cables to/from battery or to alternator. Might be bad alternator.

Take the battery to Autozone to be checked.

I have a used 2006 Chevy Cobalt. My car wouldn't start yesterday after work. So, a tow guy came out and tried giving me a start. It wouldn't work. However, my dashboard said,"Battery saver mode and check charging system". The ignition would only click. The lights on the radio and dashboard started going crazy. The locks were making sounds. The bells would go off if the doors were open. So, is it my starter? Obviously the car has some power. Or is it the battery? I need to know ASAP!