2000 fatboy starter problem

I have a 2000 fatboy with 38,000 miles and have yet to turn a wrench on her except for regular maintenence.

I have a problem with the starter that just popped up and cant find anyone with a similar problem.

When the starter button is engaged it clicks loudly. Battery is full charged, I assume since it is clicking at the starter, that the relay is fine.

Connections look fine.

Solenoid?????????

Clicking

The continuous clicking is usually either a low battery charge or bad connection. I know you said there is a full charge but have you "load tested" the battery to see if the voltage drops off? You could have just one bad cell in the battery where it appears to have a charge on a regular volt meter. If the battery has never been changed in 38,000 miles and five years, that would be my first guess. You could also try jumping it from another vehicle momentarily just to see if it still clicks or turns over. I had a similar problem with a Sportster and replaced cables and what not just to find out it was a bad cell in the battery. It appeared to be at full charge but would drop off drastically when a load was applied. I changed the battery and everything was fine.