I have a heat pump and they usually require a different type of thermostat than a normal A/C & furnace installation. Check you thermostat literature to see if it is for a heat pump. Most will say "not for heat pumps." This is because heat pumps often have auxillary heat coils.
Put the old thermostat on and record the wiring colors for the heat and cool and fan wires. The 24v is usually red. If the same connections on your new thermostat do not work, you need to buy a different model.