My husband has a 2003 Alero. We have had no problems other than the front bearings needing replaced. On Monday he went to leave for work and the car woud not start. The lights and radio would turn on, but the car would not turn over. There were no clicking noises or anything. Later in the afternoon (after it warmed up outside) I was able to start the car up without problem and drove it to have the battery replaced thinking that was the problem. Tuesday we had the bearings replaced so the car was at the shop and we did not attempt to start it in the morning, however they did not report any problems starting the car when going to move it into the garage. Then again this morning (10/22) when he attempted to start the car the same thing happened. After returning home from work in the evening he was able to start the car without difficulty and had the alternator checked it was fine. Any idea what the problem might be??

Check the grounds. If they are loose or corroded, it can cause your symptoms. If they are okay, I would have the connections at the starter solenoid checked. The solenoid itself could also be going bad.