2006 cobalt LS engine cooling fan doesn't turn on

Yes, I would first check all the fuses and your fan motor to see if it works, turn on the engine and then turn on the A/C to check the fan motor. If that doesn't work, you can use some wires and the battery. Find the fan relay in the underhood fuse box. It should be labeled as such. With a volt meter, make sure that you have 12 volts in at least 1 of the relay terminal slots where the relay plugs in to the fuse panel. Then make sure that you are getting a good ground by using the volt meter and turning on the A/C which should energize the relay, with it still out. Of the remaining slots that DO NOT have 12 volts, one of them should go to the motor and another to the Computer. Using the OHM meter on your volt meter, connect the black lead to the battery ground and the other to the slot that is the computer, if you are not sure, try both, but DO NOT put your OHM meter in the voltage slots. When you turn on the A/C, 1 of the slots should show continuity with ground. Check it at least 5 times to be sure, if you do see a good ground signal and you have good voltage, good ground and a good motor, buy a new fan relay, they aren't too bad 20-30 bucks. I hope that you can follow this, as this is close to what I do when I am inspecting a cooling fan error.