car won't crank.

Ok so what if neither the starter or the power supply is the problem. What else could it be ?
If compression was the issue the engine would need to turn a little bit to create compression. A slight turn is more than the "click" you stated. Timing chain jumped or broken would still allow the crank to turn a little. Only a cylinder filled with water could completely prevent the slightest rotation. In that scenario removing the plugs would result in water shooting from a plug hole when it turned.
I would rule out the battery and its cables/terminals, including where the ground cable attaches to the block before removing that heavy starter again.