A starter solenoid has a winding that, when enough current is passed through in the appropriate direction, shoves a plunger and makes contact between two plates. The contact allows current to flow through the starter. if the winding is damaged - it will not start. if the contacts are damaged - it will not start. if there is not enough current to hold the plunger engaged - it will not start. (that's why you hear rapid clicking when you have a weak battery). And rebuilt starters work just as well as new, barring any heat-related damage to the coils.