I am not familiar with that motor but I would always check the centrifugal starting switch first. It is possible that it was not making good contact all of the time before and the action of working on the unit got it working again for a while. We used to joke a lot with vacuum cleaner customers who would have a cleaner that had stopped coming on. It was fairly common for folks to drag a non running vac in and we would plug it in and it would run. We learned very early on to always plug in any cleaner that "just quit starting" while the customer was watching... They were usually shocked and embarrassed when it would come on. We would joke with them about next time put in the car and take it for a ride...
In those cases it was usually a bit of grit locking a carbon brush in its holder. With conventional motors it is very often the centrifugal start switch.
We just did a recent discussion somewhere here about how capacitor failure is fairly rare. The do fail but if the motor will hum then the centrifugal start switch is the the starting point of checking it out.
I did not equip with Shopsmiths in spite of the setups but because of them.
1 1988 - Mark V 510 (bought new), 4 Poly vee 1 1/8th HP Mark V's, Mark VII, 1 Mark V Mini, 1 Frankensmith, 1 10-ER, 1 Mark V Push-me-Pull-me Drillpress, SS bandsaw, belt sander, jointer, jigsaw, shaper attach, mortising attach, TS-3650 Rigid tablesaw, RAS, 6" long bed jointer, Foley/Belsaw Planer/molder/ripsaw, 1" sander, oscillating spindle/belt sander, Scroll saw, Woodmizer sawmill