I believe I have a millisecond of 120 vac on start up but it happens so quick it was difficult to detect.
Will it's dead simple to check - just measure the AC voltage across the capacitor - while the motor isn't spinning. The meter should read full mains if the capacitor is duff, and the switch is OK. I'm rather concerned that you only got voltage for a millisecond or so?. I'm presuming you've measured across the capacitor on ohms?, and it's not S/C?.I'm waiting on a new capacitor, the motor hums but will start by spinning the shaft.
The centrifugal switch works fine as I can see it open and close.