I know very little about HVAC, but it seems odd to me that the start capacitor would keep the fan from starting. It would certainly stop the compressor from running if defective, but the fan is a fairly low Amperage device. I didn't think the fan relied on the start capacitor at all?
dsaint, I may be wrong about this too, but doesn't your A/C have a fan only setting? Have you tried that? To me, your symptom sounds like a bad fan bearing. Fan motors have very little torque and if there's any resistance to motion when they are starting, they don't turn on their own. But, if you can nudge the fan blades and start them turning, you overcome static friction and the motor's torque increases as the speed of the fan increases, above a standstill.
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2014 F150 Platinum 4x4 3.5L EcoBoost SCrew