Hi Bruce,
75% of the time its just dirty or burnt contacts on the start switch. If there dirty rip it apart and clean with a thin file or fingernail file, if there burnt then take the switch and the motor make and model numbers to your local motor shop and pick one up, they are fairly cheap. 20% of the time its bad start capacitors, if the switch looks good and the throw out has free movment then you can take the caps to the same shop and have them tested. The other 5% of the time its a burnt start winding, which would require a rewind. Unless its a special frame motor it would probably be more economical to replace rather then rewind.
Tom S.