Check your POSITIVE batery lead!! PICS ADDED!!

[boreas7]

I had a similar problem on an Air Cooled 911. Intermittantely the car would not start and just ' clicked' on trying to turn over,

This went on for months and a replacement starter motor didn't help the problem, at the time I could find or see nothing amiss and the problem went away next time I tried to start the car.

Eventually I found that I had a poor connection where the positive battery lead went into the lug that attaches to the battery terminal. The voltdrop across this high resitance just prevented the starter motor from being energised. I resoldered the lug and as was well. Luckily my high resitance joint didn't create enough heat to induce burning.

[Rp0thejester]

I had that problem in a transit van, filled the tank up, wouldn't start, was a dodgy positive connection on the battery

[Carole_Heard]

This is a result of using crimp terminals and untinned wire.
DC circuits attract atmospheric ions that provoke corrosion in the positive side of the circuit. This eventually causes the copper in stranded wire to develop surface corrosion, insulating each strand from its neighbours.
Crimp connections make electrical connection to the strands of the wire in contact with the crimp, relying on the contact between strands to carry current throughout the bundle.
If the strands are insulated from each other, only the surface strands carry the current down the wire to the terminal which may have the same problem, except the strands in contact at this end might not be the same ones as at the other end.
The net result is that the resistance of the big thick cable is increased, sometimes very dramatically.
Cures:
Use tinned wire: Expensive in production
Replace the cable
Get a blowlamp and fill each terminal with solder making sure to flux everything properly so all strands are in contact with the terminal.