Anti-theft light is on?

Hello again.

I would first suggest performing an anti-theft, security system reset. Here is the tutorial showing how to perform this:

https://www.2carpros.com/articles/how-to-reset-a-security-system

Just curious to know if the check engine light is on? Here is a tutorial showing how to check for codes if the check engine light is on:

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Here is another tutorial for you to view showing a no-start condition:

https://www.2carpros.com/articles/car-cranks-but-wont-start

In case there is an issue with the wiring on the anti-theft system I've attached a the wiring diagram below for your Cobalt. I've cut the picture into 3 pieces so you can view larger. Here is a tutorial showing how to test wiring.

https://www.2carpros.com/articles/how-to-check-wiring

Hope this helps and thanks again for using 2CarPros.

Danny-