This same question gets asked and generally answered on a regular basis, and the archives can be searched thru a Goog Group search.
The Start capacitor in a capacitor start split-phase motor needs to be rated for AC, and the value of the cap should be in the range of 500uF per HP, or likely 500-750uF for a 2 HP size motor. Additionally, the appropriate cap will be rated for 120VAC or higher volts AC.
What you saw leaking may or may not be the capacitor electrolyte, but since you haven't disassembled the motor, it's mostly speculation. There could be a sheet of insulating material glued to the inside of the cap cover. Only Eyes On will determine what it is.
As you won't know anything about the condition of the motor if you only replace the Start cap, you should be prepared to disassemble the motor, especially after 30 years of use.
You should examine the mechanical parts of the centrifugal switch mechanism for wear or any other problems, and repair the parts if necessary. The centrifugal switch contacts should be closely examined, and smoothed by burnishing them, which is a better practice than filing or sanding them, which leaves sharp ridges in their surfaces which tend to melt.
Bearings are cheap if the motor is ball bearing equipped (most likely).
An internal cleaning can remove some dirt from even a TEFC totally enclosed fan closed motor. There may be loose paint, rust or other debris inside the case, and significantly more dirt if the case is vented.
An ohm meter doesn't give any useful information about the condition of a motor capacitor, unless the cap is shorted.
To confirm that an open Start cap is preventing the motor from starting, the capacitor can be bypassed, with a safe, properly insulated connection (for the dimmer ones that may read this, that means: Not a screwdriver or other hazardous method), with the load removed from the motor. Remove a drive belt or gear to separate the motor shaft from the machine.
A bypassed cap will allow the motor to start without a load, if the cap is open internally.
A capacitor start split-phase motor will start and run normally with the Start cap bypassed, and without the usual load applied to the motor.
The purpose of the Start cap in these motors is to increase the starting torque rating of the motor to meet the application. With the load removed, an good motor in otherwise undamaged condition will start and run normally.
Other internal problems mentioned may prevent the motor from starting, which is why one should be prepared to remove and disassemble the motor for inspection when any problems arise.