I have a 2006 Cobalt that I bought with 25000 miles on it. It now has 50000 thousand on it. It has always had a weird clicking noise when I turn the key off. The noise is either coming from the steering column or under dash. When it does this the switch will sometimes get stuck half way back---I wait for the clicking to quit and it will go all the way back and release the key. I have had one instance where the key would not turn the cylinder. I just had the car in for the power steering recall and they did not mention any other outstanding recalls.
If this clicking started only after the power steering recall repair, I would send it back to them and state that info to them so they can check it out.
The Cobalt has a steering wheel lock, even though the dealership may tell you otherwise, the position of the wheel in locked position is either facing right or left, its not in the straight position like most other cars, this would cause the key not to turn, next time this happens, check the wheel see if it can turn, if not move it left and right while turning the key.
I also had this issue when I made a copy, I guess it was cut wrong, It would happen all the time, I would pull the key a little out of the cylinder while turning, it would catch, I recently made another copy and it works fine, it could be the key, maybe.
What kind of click noise, something similar to the signal clicking?