2002 Saturn and good battery will not hold charge

I have a 2002 Saturn SL2 that I bought used over a year ago with no apparent problems. One day while sitting in a parking lot, with the engine idling, the engine cut off. I was able to start it right back up but thought that was strange. The next morning, I went to start the car for work and it would not even turn over. The battery was completely dead. I've been told that the battery is good and the alternater checks out okay. When I get a jump the car appears to run fine. I can turn it off and restart it just fine, but when it sits for hours, it will not start back up. What could be the issue? Someone told me that the battery cables could be corroded and that is where the connection is being lost.