The above {heat pump} unit will run outside but the blower will not kick in on the inside. What could be the cause

You need to check to see if you are getting 24v from the thermostat to the G circuit at the blower unit(blower relay or control board) Will the blower run if you turn the fan switch to on at the thermostat?

Bad bower motor
Bad blower relay.
If the blower motor will start by hand(CAUTION BE VERY CAREFUL) and runs it could be the capacitor for the motor.