A starter motor can take up to 300A surge current and typically 80A turning the engine over - it needs a high current switch to manage the power. The click is very probably this starter solenoid switch operating.
If the engine fails to turn over then either the starter motor is broken - the current path to the starter or its earth is poor or hopefully, the starter is just jamming up against the engine's flywheel. Put the car in gear and manually bump it forward an inch or so to help the teeth to mesh. This takes little time, costs nothing and it may work.
Good luck...
Peccavi
December 2009
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