Small Engines (Lawn Mowers, etc.): briggs engine, cable ends, battery terminals

Question
accidently hooked up battery wrong (positive post hooked to neg wire etc.)--tried to start 3-4 times and discovered problem and reversed wires. Now it sort of clicks and won't start. New battery meters 12.4 volts. what could I have damaged???????

Answer
Have you checked the starer gear to see if it is stuck?  Expose the starter to observe if it turns.  As it turns, does the starter pinion gear turn and rotate upwards?

If you connect another battery, does is still just click?  Did you clean both the battery terminals and cable ends with a wirebrush before you connected the battery?

Let me know.
Eric