possible fuel pump issue with 2010 chevy cobalt?

Doesn't take much power to run lights and radio. Check battery voltage first. Charged battery should read 12.7 volts. Discharged is anything under 12.2

But... if there's enough power to turn the engine over, there's likely enough to make it run. While you're checking the battery check the connections as well to make sure they're tight. Then listen for the fuel pump running for a few seconds when you turn the key to the run position without trying to start the car. If you hear it its probably fine. If you don't then its possibly a failed fuel pump or something in the wiring controlling it. Testing the fuel pressure is helpful if the pump runs but you still suspect its not getting fuel. While you're testing things scan the car for trouble codes. There may be information in the computer that will guide you. Most of all though is to find the problem before you start replacing parts. Randomly changing parts in hopes of accidentally fixing the problem rarely works and gets grossly expensive in a hurry. Good luck.