If it was a relay then on mine it should go in and stay there. On mine the power button also trips when the chuck shield is raised or the gear cover is opened. When you press the power on button it normally clicks if all the cutouts are closed but in the cold weather it doesnt click until its warmed up. I would have thought a relay would not be affected by temperature.
The direction reversing switch is separate. On mine if you flip the switch when running you will blow the start capacitor(did that once).

Peter