Fan is now turning after I nudged it with a screwdriver. However, air is not cooling.

Likely a failed dual capacitor. The compressor may not be running. The pic shows a failed capacitor on the left, a good one on the right.

Thank you for confirming this. Two questions remain: is there something I need to investigate regarding the cause or is typical for a 7-8 year old system in the hot south? And what is the easiest way to get a replacement part? The part is made by ge and looks almost exactly like the ones in the photos but I don't know which numbers are the part or model numbers.

The replacement brand doesn't matter, and the actual part # will vary from brand to brand. Match the replacement to the ratings of the voltage (370 is most common, 440 would be more reliable) and capacitance (#'s followed by "UF"). Try to stick with the same shape (round or oval) for ease of installation, and make sure the wires are connected to the proper terminals (they are marked "FAN", "HERM", & "C"). Disconnect power to the unit before touching anything inside the control compartment. Failure of the existing capacitor may be the result of a line voltage disturbance that occurred while the unit was running, and does not necessarily indicate a problem with the unit.