Hi bettyboop.... Don’t know about the roper and said so. But, our friend with the problem as well as I would have appreciated an answer to his problem. However, if you want a discussion in details let us have one.
Talking science, there is nothing in our universe is called burned out capacitor as every thing in universe has a degree of capacitance, including human body and even the burned out light bulbs. If you cut the capacitor in two, put half in Japan and half in USA it will still have a degree of capacitance (scientific fact). What happens is that the capacitor loses its capacitance to some degree, depending on the level of damage to its dielectric material.
Talking washers, many washers do have integrated capacitor block that incorporates resistors and coils as well as the capacitor. For this kind, damage to a resistor or a coils could lead to a full black out of the whole block. This doesn’t in any way prevent the capacitor from having the fault and losing some of its capacitance.
Talking DIY, I advice our friend to buy a multimeter that can measure capacitance, over ebay it would cost about $20 (you always need it). Or take the capacitor to someone who have one to measure its capacitance value, compare it with the printed value and replace if it is less the 80% of the printed value. Good luck. | 
