I've been studying on my unit recently because I think the compressor motor starter windings have failed.
We'll be getting a new compressor under warranty shortly.

Some observations- when all is running the air blowing out of the outside unit should be a lot hotter than ambient. That's just sticking your hand in the airflow. (when my compressor didn't start the fan would run but without compressor there's no extra heat)
In the house the copper line to the evap coils is very warm to the touch but not too hot to touch. Cool air (but not cold) comes out the ducts.