Lou,
I had something similar on my K75S, a long time ago. Don't recall the exact symptons but had to jump start it a couple of times cause the lecky start button did not play.
The solution was to pull the starter motor, strip it down and give the surface of the coils/wiring? a good clean with white spirit or something similar cause they were pretty dirty. Solved the problem.
Hope this helps, Burt.