I have attached a photo of the back of the board and drew a boarder around N313. You are correct that the middle pin is not used. If I test the two outer pin on the tester, the screen indicates that it is a diode?
Also, I found some broken traces where a plug inserts and have soldered some wire leads to repair the. The heat now works.
When I plug the unit in, the air pump works for a minute, then shuts off, which is normal. When I turn the unit on, I get heat and airflow, but cannot adjust the speed and the LED indicator does not light up. If I power off the unit, the air continues for a minute then shuts off, which is normal.
Steve