Q: Car won't start - only clicks when key is turned.

After pulling into a parking spot and putting my Kia into park, the engine suddenly died. Now it will not start. When I turn the key, I only hear a single, loud click. All lights and radio work. I had the battery tested at an auto parts store and it was fully charged. I cleaned all corrosion from the battery terminals. About a month before, my heat/a.c. started acting up. Blower would not work 80% of the time. Not sure if that's related. A good Samaritan stopped and turned the engine? by hand. My engine started to crank, then went back to the click. He said he thought it was the started, but he was not a mechanic. Is the starter the most likely culprit here, or could it be something else?

My car has 65000 miles.
My car has an automatic transmission.