"At this point, with this description I am sensing two different
problems. "

Who are you, counselor Troi?
Or are you vulcan? Do you meld with HVAC equipment over the internet to
sense it's problems?

Anyway everyone knows what problems you are going to say need fixed:

1) A used, incorrectly sized capacitor must be installed somewhere,
probably someplace behind the thermostat.
2) A circuit breaker - ANY circuit breaker, needs to be replaced with a
different brand, chooped up and then crammed back in the service panel.

Duh.