Sometimes - quite rarely - the teeth on the bendix gear of the starter motor jamb up against the engine's flywheel instead of meshing with them. You can overcome this by putting the car in gear, taking off the handbrake and bumping the car forward - just an inch - with your bottom. It's worked for me about three times!
It will not be a belt thing - belts are not involved.
On top of the starter motor is a big power relay - when you try to start you should hear it click.
If the starter is taking current then the headlights should dim as the battery voltage drops.
Check also for a flat battery.
Good luck...
Peccavi
December 2010
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