Small Engines (Lawn Mowers, etc.): Reversed battery polarity - now wont start, craftsman lawn tractor, jumper cable

Question
I have a Craftsman Lawn Tractor with a B&S engine. Unfortunately, I recently replaced the original battery and accidentally reversed the polarity of the battery cables. The next day when my wife attempted to start the engine, it would not start. That is when the error was detected.  She was able to correct the polarity, but the engine would not start.  Several hours later, the engine did start allowing us to back it up into the garage.

However, now after our week vacation, we return to find that the engine will not start. I turn the key and it merely clicks.  Is this a solenoid or starter issue?  Thanks in adavance.

Answer
 Hello Dan:

 Take a Jumper Cable Set and Attach the Red Lead to the Positive Side of the Battery. Take the Other End and FIRMLY Touch the Battery Post of the Starter. If the Starter Turns, then the Soleniod is Giving Problems. Take the Jumper and Place One End on One Side of the Soleniod and Use the Other to FIRMLY Touch the Other Side of the Soleniod. If the Starter Turns the Soleniod is Bad. Is the Battery Staying Charged? Usually when a Battery is Reversed to Ground and Left that Way the Battery Shorts a Cell and Wont Keep a Full Charge. **Check the Battery First for a Bad/Weak Cell**. Hope this Helps. Let me know what Happens, Please.

 Good Luck

 Respectfully

 John