If you meter across the solenoid posts when you press the S/S button, does the battery voltage go through the solenoid? If so, then the problem lies beyond the solenoid......the next suspect is the wire from the solenoid to the starter and then the starter itself....
The click is telling you your ski sees the battery voltage, the button push wiring path is all connected, the solenoid MAY be working (the solenoid may click but if it is NOT passsing the voltage through it, it could be burned or carbonized internally - however, not very likely if its brand new)......keep following the voltage path through the solenoid through the wire to the starter....you are almost there.