Although mine is a different model I had something very similar.
One day, out of the blue, it just wouldn't turn over and I got a click from the starter motor.
As the starter motor was 40 years old I changed it for a known working one (on the bench anyway) and got the same fault. I knew the battery was good as it was fairly new so I checked the voltage to the starter through the main thick cable.
I had 12 volts at the battery terminal and 1 volt at the starter! The cable had deteriorated over the years and was creating a huge resistance to flow. Changing it cured the problem. This also happens to earth cables!
Hope this helps.