Hey mate,the click you can hear is the starter solenoid.Its basically the bit that connects the starter motor to the battery.
The battery seems sound and the solenoid sounds like its working,so.......have a look at the starter motor connection.Its under the front of the engine and collects all the crap off the front wheel.(You will probably need to whip orf the fairing)Pull the rubber boot off the connection and check for corrosion.
Are you about in the daytime?I could maybe nip round and have a look if you like.
