Usually when the start capacitor on a AC motor (batteries are DC), it's pretty obvious. They are also pretty cheap (under $20). Motors, one with enough horsepower to mix cement (mixed 11 X 80 lb bags by hand last week), I'm guessing $200- $300....
Anyway, if the start capacitor looks damaged... Swollen, top popped off, terminal missing, leaking fluids... might be a cheap repair.
Now, the motor... Well, if not overworked, its most likely fine. Don't know how old, or how much work its seen. If you use it professionally, 8-10 hours a day, 5-7 days a week, and only service it when there is trouble... yeah, maybe.