If this is a shaded pole motor.
I would not discount bushings in the motor, especially in the environment of the fan (and its long time in service), shaded pole motors are used in a lot of smaller fans and motors, these motors normally will not burn the winding's (almost never).
Not all shaded pole motors are thermally protected, (even the ones that are not thermally protected normally almost never burn their winding's).
Those that are thermally protected are normally a bit larger style of the shaded pole motor, that pull a little larger fans or other machine... These motors primary winding is more prone to overheat on startup or under a higher load, or with lack of lube in the bushing, thus the primary coil is protected by a thermally operated switch to keep the coil from overheating and burning out your motor, kind of similar to a reset-able circuit breaker that works with heat instead of current...
They do not have start winding's, a start capacitor, or a starting switch (mechanical or current).
Their construction and how they operate is different from most motors.
They use one winding that is powered from your household current on poles, one of the poles has a copper ring, which shifts that poles current and magnetism to make the motor begin turning in one direction, this primary coil is normally of heavy enough wire and insulation that it can handle a locked rotor condition, IE: the motor not moving with current applied to this primary winding, and not burn off insulation of the coil, or burn into or short out this winding, and those larger shaded pole motors that have thermal circuit breakers to protect the winding insulation from getting too high or hot, and burning off...
The other winding (in the rotor, does not see household current, the current in this winding is induced by the primary coils winding's and the magnetic field the primary winding moving or cutting across this secondary winding (note the magnet moving is important here), with out that movement or fast enough movement the motors primary winding will pull more current which also generates more heat (watts).
The bushings must be in good shape, be lubricated so the rotor can turn extremely easily, especially when power is applied at the first, for startup when the motors primary is going to pull a higher current, and the magnetic field is weak because of the magnetic field and it relatively slow movement of the magnetic field until it get to running up to (full) speed (full speed is also important here).
The bearings are like the lever in a machine it is the weak point in a mechanical lever, just like in a sea saw lever where a small boy can lift a heavy man on the other end of the sea saw, just a little less weight on the boy and the large man just sits there, without oil or free movement in the bushings your motor will just sit there and warm up...
Spinning the motor by hand your are overcoming most of the friction keeping the motor from starting, Your also making the primary's winding magnetism cut faster across the secondary winding which creates more magnetism in that secondary to keep the motor running, but friction in the oil-less or oil starved) bushing is still putting a drag on the motor, (the boys weight is not quite heavy enough to lift the big man fast or good enough) so the primary winding is also having to work harder to try to get up to full speed (which it cannot do without good movement at the bushing) pulling more current and generating more heat (watts)...
Basically if it is a shaded pole motor, you have, the problem is normally lack of lube or friction in the bushings, or bearings, they almost never burn out the primary of the poles, and do not have many of the parts other types of motors which can go wrong. Taking the shaded pole motor apart and cleaning and lubing it will almost always get them up and running again.
Shaded pole motors can also be reversed easily by turning the rotor around,(the center rotating portion of the motor with the secondary coil which get its current from induction of the magnetic field) and its relation to the shaded pole with the copper ring coil of the primary's shaded pole. So if it turns backwards after you have oiled it and put it back together just take it back apart and turn the rotor around to get it spinning in the wanted direction.
These motors normally do not have good starting on most any kind of external loads, so that also limits there use in many things that need motors, small fans are a good application for this type of motor, and in most smaller fans you will have this type of motor.
Your's may not be a shaded pole motor, so much of this may not apply, but it would not hurt to try, even for fixing up a backup motor for your hood.
Simon007, you are correct in what you said.
And I do not wish to take anything from it as it is good advice.
But I still have to disagree somewhat, depending on the type of motor, if a capacitor or a start switch is bad the motor can overheat or get hot, the start winding can over heat and begin to burn out, the run winding cannot get running fast enough or soon enough (even with the help of your hand spinning it, like helping the young boy on the sea saw by you standing on the big man side and helping lift the big man so the boys weight can pull down slowly on the sea saw with the inertia you created on that side of the lever...).
When trouble shooting I do not discount any possible problem completely, even the ones that are probably never a problem, I keep them in the back of my mind so that I may be able to check to see if they are actually the cause, and many times they are, and they are the ones we can very easily overlooked by our own disregard.
You could paint it black or something to hide the green color and make it blend a little more with the roof..
