[Coffin Dodger]

I cleaned the Road King with a pressure cleaner but with the pressure turned right down. All the familiar lights and sounds come on when I try and start except that it doesn't start and I just hear a click when I press the start button. I let the bike dry out and still she won't start - incidentally, there's no fault code.
Am I right in suspecting the starter motor/solenoid and if so, what is the remedy.
Other than that, can somebody give me the logical troubleshooting sequence to trace and fix the fault?
thanks