You can check your heat pump on the outside by turning off the power and listening to see if it makes a whoosh sound. and then turn it back on you should hear it kick in. Is the outside unit running? Sounds like an electrical problem maybe in the breaker or the contactor on the inside of the unit. This is where the 24 volts from the thermostat call to the 240 volts to kick on the condenser fan and compressor. Be real careful in messing with this because of the high voltage.