engage. What could be wrong? The HVAC guy already changed out the little $20 capacitor. When he engages the switch at the outside unit manually, it turns on, and functions properly.

But, when you try to get the system going at the thermostat, the outside unit won't engage.

He wants to change the thermostat to a new one, but I can't see how that would be the issue. Is there a mechanical device on the outside unit, that connects to the thermostat that could have failed?

What other options are there?

Freon is fine.