WELCOME to LMF...
Please DON"T use all upper case on your posts... (Not easy to look at, or read).
I think you May have left out a letter or # in your model, I don't find anything for
13AN77K011...
I am guessing this is your LT... and this parts illustration shows a couple things to check...
Parts and Diagrams for Troy-Bilt 13AN77KG011 Pony (2009)
Have you checked voltages at the starter solenoid? (item #57) Large terminals & small terminal, With key switch being held to Start? What voltages do you get?
Your problem likely has to do with (item #58) interlock switch... check that everything is hooked up and actuating... :smile:KennyV