Small Engines (Lawn Mowers, etc.): Craftsman mower will not start, batt good, battery connections, flywheel

Question
I have a craftsman rider model #917271552 with a 15.5 hp B&S motor.  It is 3 years old and has been garage kept till a month ago (just moved).  It has been sitting out side but covered.

Ok, the battery finally died and would not recharge.  I replaced the battery with 350 amp model.  

When you turn the key the starter will spin (fast!) but the gear will not rise up and engage the flywheel.  The engine will easily turn over by hand (rotating from top).  I have already soaked the top of the starter in lubricant and manually made sure the gear will rotate up the shaft.  Also, a small red wire that goes under the cover to the starter gear area was hot to the touch after about ten attempts to start.

What do you think the problem is and what should be my next coarse of action?  Would sears have the part(s) in stock?

Thank you!

Answer
Did you check the plastic starter pinion gear.  You may have to remove a cover to access the starter pinion gear.

When you turn the key does the starter gear climb up and engage the flywheel?

Is the battery connected backwards?  Even the best of us have done this at least once.

Check the battery connections...if they are backwards the starter will spin backwards.

Let me know what you find.
Eric