Mower model number 13AV60KG
Engine model number SV540S
Excellent so you have a modern Troy Built Tractor with a Vari drive powered by a Kohler vertical engine.
So the easiest & quickest wat to work out wat is happening is to get a can of starter fluid and an inline spark tester.
Instal the spark tester crank the engine and squirt a
SMALL SHORT blast of starter fliud down the carb.
Watch the spark tester for a consistant flash.
If the engine starts up keep on applying the same
SMALL SHOTS of starter fluid down the carb.
If it keeps on running for around a minute shut it down.
You have just diagnosed a carb problem.
No flashes or eratic flashes
you have just diagnosed an ignition / electrical problem
Flashes but does not fire , dackfires, pops or other such nautiness.
You have just diagnosed a timing , or valve / cam problem.
When you get back to us , try to avoid phrases like "won't start " which is fairly well meaningless.
Cranks but does not fire, wont crant etc, a lot more descriptive.
You know what is happening we only know what you tell us.