See if this helps. Since the motor is not froze up, good, then what's next?
Yes the fan start capacitor may be the issue but the control board may be the issue as well.
You can test the control board to see if it is sending 120 VAC up to the fan to even start.
Before you start any of this, you need to know 12 volt DC and 120VAC skills before attempting any of this. If any of this it beyond your ability, stop and take it to an electrician. I will not have every step you need to do, but point you where to look if you are electrically knowledgeable. Make sure the power is off before testing. There is a 20 amp breaker in the power panel.
Here are 2 wiring diagrams. The roof unit
The inside control board
The control box is inside up in the air box. Looks like this. This pic is already out of the air box area.
The cover off
The control board itself so you can read it
There is a low and high fan wire. Red is low speed fan and black is high speed fan on the PC board itself. They are push on blade terminals. The relay on the control board sends 120VAC power to those 2 wires at the correct time. If you unplug the low or high from the board, you can meter test or test lamp test the relay to be supplying 120VAC when the fan should be on. The controls run on 12 VDC so the battery needs to be on when you turn on the T stat, the control board will work. You will be able to hear the relay click, or at least the compressor one as it is larger.
To test the fan motor on the roof, with the breaker off, unplug the red or black on the low or high fan wire and jump it to a hot wire. Turn the breaker on and the fan should start. OR You can also use a 120 volt light bulb or a meter as this is s simple relay.
You can grab 120 VAC on the compressor relay. The heavy black wire is hot when the breaker is on. Blue goes out to the compressor. If you do not want to power up the compressor, pull the big blue wire off the relay. Or even easier, just slide the T stat switch to fan only to run the fan manually.
See my jumper here the low speed fan wire and to the hot on the compressor relay.
If the board is working, then the problem is up top on the roof unit if the fan will not start.
The start capacitors are in the rectangular box on the side of the roof unit. There is usually a hornets nest there too, heads up. Seems that way every time I'm into one.... The wiring diagram I posted is on the outside of the box
On the fan, if you have an older analog meter you can test if the capacitor is toast. You can see my old blue one in the back ground.
Heads up, if the capacitor does not have a resistor across the terminals it need to be discharged before testing.
Page 28 of this PDF talks about testing the capacitor
Page 27 talks about shorts or open wiring on the fan motor stator tests. You can test to see if the motor has an open circuit to AC common or a dead short.
http://www.nwrvsupply.com/manuals/du...at_service.pdf
Rather then me typing it, you can read those 2 pages and it should get you honed in to the right area.
Hopes this helps and let us know how it goes.
John