The thermostat is 12 v, powered by the house batteries. Make sure any battery disconnect switch is on. The furnace should be controlled by the thermostat and is also 12 v, LP gas burner with forced air fan. The A/C is 120 v, and if no controls on the ceiling is controlled by the thermostat.
Check that furnace fuse in house fuse panel is good, if standing outside next to furnace while someone else has thermostat on 'Heat' and pushes temperature selector down it should trigger on. First the fan will start, then ignitor should snap and gas flow.
If you do a Google search for your make and model of A/C, furnace, and thermostat you should find manuals available online. Good luck with it!