Well, Goodman GSH 130241A is a heat pump and the inside coil could be warm but not in the cooling cycle. For it to be actually cooling the house the HP should be in Cool mode and the inside coil should be cold, not warm. The <i>outside</i> coil should be warm. So, is the thermostat in the "Cool" mode? I know this is probably too basic, but I just wanted to get this out of the way so we can look at actual potential issues.
You have two identical thermostats for 2 heating/cooling zones and you swapped them in their plastic cradles with contacts on the back to eliminate a possible thermostat malfunction - did I get this right?. So, do you have two outside units / two inside air handlers then or is it one and the zones are controlled by damper valves?
Have you shut the power down to all parts of the system (indoor, outdoor, 24V control transformer if on different circuit) at the house breaker panel, waited a few minutes, restored the power and observed what happens? Any changes?
The outside fan runs. Do you hear the compressor (below the fan) hum, too? Any suspicious noises? Does the compressor start to run, then goes off? Do you leave it on "cool" like that for a long time, even though it's not cooling?
So, there are few more things you can check before someone needs to hold your beer :)