When electrolytics fail, it is usually because a voltage was applied that was either higher than the rated value of the capacitor or of opposite polarity it was made for. Large value capacitors are used in the power supply, so you might find that transistor(s) or diode(s) were already blown and this took out the capacitor. Possible reasons include shorted rectifier diode(s) and open output transistor(s) allowing the power supply voltage to rise past the voltage limit of the capacitor.
What I thinmk you might want to do is to remove the transistors and diodes and check them out of circuit. If you have a schematic, it will help you find the parts that are most likely to have failed. But even without a schematic, you can check the transistors and diodes. Be sure to remove them from the circuit when testing.