This was a tricky issue to diagnose. The purpose of a factory molded plug is to ensure that the wires cannot be connected to the wrong terminal, but what happens when the factory miswires the plug?

The brand new package AC would not cool because the compressor would not startup. Adding a hard start kit did not help. The hard start relay chattered and the start capacitor got hot very quickly.

After extensive troubleshooting I found the culprit, something you would not normally expect to look for: The black and red wires on the molded compressor plug were reversed. This meant that the start winding was never receiving the capacitance it needed. After fixing the issue the AC ran normally.