The first of these problems can occur from the power draw of the pump and compressor itself.  You can easily pop a circuit break, either in your break box or on the motor itself.  This is of course after you check to make sure the thermostat is turned on to heat and the power switch for the heat pump is on.  Sometimes there can be fuses that can blow in the switch itself, you might have to check that.  If there are no power problems we can move on.

The next problems that could arise is air flow blockage in the house.  If the heat pump is running there could be closed registers or things blacking hte airflow.  Make sure everything is clear, this can include checking the air filter and making sure it is clean.

Stay tuned for some more advanced trouble shooting techniques for heat pumps.