Its a strange one alright, presume nothing daft like a 6V starter or reversed battery polarity, can you try a different battery.
If its the normal pre engaged type starter then you might have one wire going from start button to the solenoid, there will be a much heavier cable direct from the battery to the main starter terminal, when the start button is pressed the solenoid is energised and engages the pinion with the ring gear and also closes a contactor to stat turning the starter to start the engine. You could check the resistance between the solenoid coil + and the body of the starter and see if you have continuity or a fairly low resistance as I think that the solenoid coil is also connected internally on the negative side to slowly turn the pinion while also engaging it before the main contacts close.
If its the normal pre engaged type starter then you might have one wire going from start button to the solenoid, there will be a much heavier cable direct from the battery to the main starter terminal, when the start button is pressed the solenoid is energised and engages the pinion with the ring gear and also closes a contactor to stat turning the starter to start the engine. You could check the resistance between the solenoid coil + and the body of the starter and see if you have continuity or a fairly low resistance as I think that the solenoid coil is also connected internally on the negative side to slowly turn the pinion while also engaging it before the main contacts close.