When the screen on your thermostat says "low Batt" it is telling you to replace your batteries. It has no bearing on the elevation of the local bat population.
When the screen on your thermostat goes blank, it's beyond "low batt", try replacing your batteries.
If you are just coming in from the north and the thermostat is set lower than the temperature, "calling for cooling" and the air conditioning unit is not responding, "answering" check your humidistat. Most are wired in series, like the old Christmas tree lights. If one went out, the whole stand went out. Both your thermostat and humidistat have to be calling, in order for the air conditioning unit to come on.
If the thermostat and humidistat are both calling and the air conditioning still is not answering, check the breakers in the panel, they may be marked as A/C or Heat, or condenser or compressor. The breaker will be 2 switches linked together as one big one.
The other most common service call is "drain overflow switch is tripped", that gets a little more complicated, you should call, text or email.