Here are your parts, includes a wiring diagram.
Replacement parts for Frigidaire LEQ6000ES0 Frigidaire/dryer | AppliancePartsPros.com
I was hoping to see a start capacitor in the schematic.
As you can see there is no capacitor the motor.
Is the start/run centrifugal switch internal or is it replacable?
No you have to replace the motor (item 28 in Section 4)
Open the unit up just to be sure that lint etc. is not preventing the centrifugal switches from activating.
Also before ordering a motor check the belt, drum seals, internal seals, rear support bearing etc. so you have an idea what a basic overhaul will cost.
The unit may not be worth fixing if it needs lots of parts and.or is in poor shape.