That is the classic symptom of worn brushes inside the fan motor. A clue is it will often start working when you bang on the heater box. Once it starts running, it will not fail to continue running until you turn it off.
It is possible for an overheated connector terminal or fan speed switch to cause intermittent operation too. But those do not take long before they become a permanent failure.
Sunday, January 8th, 2017 AT 3:02 PM