We're just guessin' here, because we're going on your description, but most likely, the fellers have it pretty much right. It is likely the starting contactor switch. Don't be calling it a solenoid--that is a very specific kind of electrically driven contactor switch.
The starting contactor switch is easy to replace and you will know immediately if that was the solution. If you replace the switch and the ol' girl still won't crank when you mash the starter pedal, then you got some wires in the starter motor that are not right--commutator, brushes, field wiring--work for a professional.
