1. Always begin at the beginning...
2. The capacitor is NOT the beginning...
First you need to be sure you have power. You have done that here by flipping it on and having a hum. It is OK if you hum but never allow a motor to hum. It really messes them up. Flip it off quick.
"ALWAYS" suspect the centrifugal starter switch first once you know that you have power to the motor. See Bill Mayo's comment above about a mallet and compressed air.
If it is good only then suspect the capacitor. See Bill Mayo's 7 years comment above.
It would be well if Shopsmith started sending out decals to all owners to be placed near everyone's on-off switch that said "It probably is not the capacitor"...
Maybe there should be a header that pops up on each page here that says "It probably is not the capacitor"...