Use a voltmeter and check that red (RH/RC/R terminal or whatever is used on thermostat) has +12vdc on it.....also depending on the thermo the RH and RC terminals should be jumpered together if they are separate terminals)......so if touching the RC terminal to Y terminal (which is for cooling compressor) and there is no joy......try checking that the blue (B) is grounded on the thermostat. If the thermo has its own batteries then what used to terminate on the B terminal of the old analog thermos (coach ground) has to still provide ground to the relay in the air conditioning control box......usually accessible by removing the inside ceiling escutcheon vent panel of each air conditioner if you need to get in there. Check the wiring behind the thermo first though. The fact that both air conditioners and two new thermostats are doing the same thing.....means the trouble is probably the common denominator......the person wiring missed some little thing I suspect. Maybe?