I think I understood you the first time... but I am questioning that the compressor is running, because you said that you *think you hear the compressor running...that is why I prescribed the test and especially the temperature measurement at the cold air outlet.
What you are describing points to either a bad printed circuit card or a bad thermostat... but the are also some contradictory indicators.
So I must ask for these these tests.
Or you can gain access to the units electrical panel and send me a photo of the wiring diagram and I can mark it up with trouble shooting instructions. Its midnight here, I have been up for 18hours, if you like I can stay up another few hours for you, or I can go to bed and pick your response up in the morning.
If you want to do this trouble shooting attach a well focused, close up photo of the wiring diagram glued inside the service panel,you can use the paper clip icon at the right end of the toolbar at the top of this dialog box,Include a picture of the thermostat wire connections to the printed circuit board in the same area.
If there is no paper clip icon, look for the '+attach files' link at left of your send button.
I can mark it up with trouble shooting instructions. You will need a multi meter ($30 at a hardware store) and some experience working with appliances, let me know a lot about your skill sets in those regards.
Let me know how you want to do this, we can go from there.