Been thinking about this a bit more--I used to own a Ford 6 cylinder car that was notorious for starter problems.The starter solenoids were mounted on the side of the starter right next to the 'Block and the massive ammounts of heat produced by these motors used to cause almost 100% malfunction rates.Turn the key and "Click" was all you'd get.
Funnily enough,the way to start it was to gently tap the solenoid and starter a few times to free up the bits inside---
I dont know where the H-D starter solenoid is located:i'd have to move 2 cars and both bikes to create access to the garage cupboards and my manual ;and i'm feeling lazy-but as these things produce the same excessive heat mayhap starter and/or solenoid have heat stroke?