OK... thanks for the extra info.
hmmm, why the changed out of the AC? Asking cause maybe if there was an issue, the thermostat might be at issue and was never "root caused" by anyone.
You are likely going to have to have someone look at it if you aren't willing to do some "disassembly" of some areas to get better looks at things. There are relay boards under the panel in your picture that are based on "system needs" along with how they have been connected to the wires showing.
Further, the wiring at the thermostat needs to be identified specifically to see what wiring is leaving there and going to the "jumble" of wires in your picture that ultimately need to go to the relay board that I mentioned.
Ultimately, lots of tracing / tracking to determine where the problem lies.
Since the original company isn't very "co-operative", you are likely stuck between "rocks". :-(
