Small Engines (Lawn Mowers, etc.): solenoid and starter, jumper cable, direct cable

Question
thank you for the method of testing the solenoid and starter with the jumper cable.
working on john deere LA115 lawn tractor.  At first when i touched the hot cable from the battery direct to the starter, there was no response.  after working with it a few minutes, the starter kicked in (also after loosening the bolts)  I tightened the bolts and the tractor started 3 times with the ignition, then quit again.  now the starter will not respond to the ignition or direct cable.  Is it possible that there is a coil that is bad which is causing the starter not to engage or do you have any other suggestions?  The battery is very hot, and I had a 50 amp booster hooked up to it at the time.  even when the engine turned over, it was a little sluggish.  Thanks for your help
Bill

Answer
Bill,

I dont remember this question, and reading through my answered questions cant find out more information about your problem.  I think you may have asked one of the other experts, I dont normally recommend this type of test procudere that you have described here.

Please get back to me with more info and i will help you.