I have an '05 base cobalt with a few modifications on it. Over the past few years I has intermittently not wanted to start. You put the key in and turn it to crank and nothing. No lights, no power, and you can't get the key out. Sometimes after a few minutes of wiggling the key, wheel, shifter the power will return and the key is released. The car will then start right up with no further issues. It will only do this once a month or so. My girlfriend is a social worker and relies on the car and sometimes she is not in the best neighborhoods of LA. Battery is good. Just had it replaced a year ago and tests to 12v.

 

Possibly a problem with the ignition switch in the steering column? I know a lot of Cobalts have had issues with the keys getting stuck there. There are a couple how-to threads on fixing the problem with the key sticking, but there may be more going on if it won't register to crank the car, too.