Why won't my 2007 Chevy Cobalt Start?

While driving down the road one day I noticed my radio cutting out then coming back on and that my A/C was not cooling the cab of the car (it was a hot day). I finally got to my driveway and as I turned, my power steering got really tight and my car pretty much coasted into my garage. About 15 minutes later, I tried to start the car but it would not start, just made a bunch of clicking sounds. We were able to jump the car, but it didn't stay on for long and the power steering is completely gone (felt almost like it drained the battery faster when I moved the wheel). We cleaned all the battery terminals and the ground and the battery, itself, (a good battery, by the way) is less than a year old. Could it be the alternator? The starter? Any suggestions/ideas would be GREATLY appreciated.