HVAC blower motor does not come on in either the heat mode, a/c mode. Or fan only mode. However, it comes on in emergency heat mode. Any ideas what might be wrong?

If the blower runs it is not the motor and must be in the control system. Usually a relay or sequencer.

Could be a loose connection at the furnace or the thermostat on the "G" terminal. When you switch to emergency most likely the equipment controls the blower,where as the thermostat does in the other listed options.