Hm. I'm interested now in case this ever happens to me. There could be a lot of things wrong with it...since it doesn't crank that rules a lot of things out. I would first test all the fuses and relays in the underhood ignition box. Was this car taken in for the ignition switch recall? Call the dealer, they'll be able to tell you how to check.

I guess first you should check to see if the starter is getting power. If not, work your way backwards from it:





And if you're incapable or don't have the tools, just take it to the dealer. They'll charge you $60 to find out what's wrong. I have a feeling it's probably something very simple. If your interior accessories get power but just your starter doesn't, the battery cables must be fine. Check the diagrams and let us know what you find out.