My wiring diagram for the K75 is pretty bad and doesn't show what is going on in the switches and relays. This is typical.
However, the starter button gets power from either the Neutral Indicator or the Clutch Switch. The power comes into the right combination switch on the Black wire with green stripe. If the neutral light is not lit, there probably isn't any power coming from it.
When the clutch is pulled in, power is sent to the start button, bypassing the Neutral Indicator. This allows you to start if the transmission isn't in neutral.
The power that goes to the start button comes out on a black wire aith a yellow stripe. This power goes to Start Relay, the Ignition Control Module under the front of the tank, and to the Jetronic unit under the seat.
Because the starter isn't spinning when the start button is pushed, I am inclined to believe the problem is in the wiring to and from the start button, and that is where you should look first.