Easy as pie to test the capacitor...Although finding replacements is not always simple.

You can test the capacitor with an analog-type ohmmeter, set at a high resistance scale. Turn off the circuit power first; then discharge the capacitor by placing a screwdriver or other piece of metal across its terminals.

Now, you disconnect the capacitor from the circuit. Connect the meter's test leads to each terminal. If the ohmmeter measures a high resistance, the capacitor is open and you should replace it. If the reading is zero or a low resistance, the capacitor is shorted. Again, you should replace it. If the reading is zero or a very low resistance initially and the resistance slowly increases, the capacitor is good.