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The way we test that sort of thing is to set the controls to the extremes, set the system on cooling and down to 60F.... then 15 minutes later to heating and up to 90F. tell me if the outside unit runs or not, and feel the two copper tubes attached in each case and tell me if on of them gets cold with cooling on and hot with heating on or not.
The system does not need refrigerant unless it has a leak, see if you can see any signs of oil around the copper tube connections at the unit outside or not.
I am off to bed in half an hour, if I miss you tonight I will pick your response up first thing in the morning.
We can go from there.