Visual inspection may reveal it to be bulged, or have a blown out safety plug. Usually connects to R or Run terminal on the Capacitor. Here is the one for this unit. Usually connects to C or Common terminal on the Capacitor. This applies here too. When we talk about wear and tear, it is something that adds up or weeks, months and years each time it starts.
Indoor Air Quality Investigations:
What Is an Air Conditioner Hard Start Kit?
Motor starting capacitors can hold a charge for days! The compressor starting under higher pressure differentials thus needing more torque. It doesn't have to look exactly the same and rarely does. Now I am not going to get into explaining or debate the pros or cons of solid state to the other types. Similar starter capacitors are available for air conditioning compressors.