I turn the key on my craftsman mower and it just clicks occasionally the new starter turns the flywheel a little but it won't crank please help

you either have something between motor and flywheel or belt is in a bind on flywheel remove deck and check all around.

Joel, Recheck battery to make sure it has good charge >12 v and all battery and starter wiring,plugs,connections are clean,tight and undamaged. If you remove spark plug and engine spins freely from the key, the engine compression release or valve clearance needs adjusted. It is probable the solenoid or starter is faulty, the starter Bendix/drive may be sticking. If you can, give the starter a couple sharp raps with a hammer or bar and then try to start.
Check the attached links,instruction and guides to help diagnose starting issue. Good luck
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http://troybilt.custhelp.com/app/answers/detail/a_id/86/~/clicking-sound-while-attempting-to-key-start---riding-mower
What Are the Symptoms of Bad Starter Motor on Riding Mower Engine
My Bolens lawn tractor won start It just clicks when turn the key even...
Craftsman riding mower won start Just clicks the starter motor

You said valves are OK, but did you mean not leaking and seating properly or correct tappet clearances? Check the valve tappet adjustment. If they are slightly tight the engine will be hard to turn over.

1.try jumping the battery with your car battery. I have had same issue in the past with a brand new battery.
2. Try spraying starter fluid into the carb while cranking. If it starts or at least tries to start (assuming cranking is fixed), you have a fuel problem. Again, when I first tried to fire my Used mower, had to use starter fluid to get it to start the first time, but never since.

sounds like a safety switch problem. but maybe you can help me i have the same model do you have a lot of jerking when you start off of turn with yours?

Maybe one of the pressure switches is bad

make sure thers power going into the starter
if there is then see if the starter is siezed, try turning the fly gear, but not just up against the flywheel but try turning the starter backwards to see if it moves

I have a duetz-allis mower with 18hp. kohler eng. won't start, have new seloniod, new circuit breaker, getting fire to switch & out. Still won'tstart

A couple of quick questions.
1. How new is the battery? Reason I ask is the battery can lose the voltage quickly, even though it shows good voltage it may not be producing high enough cranking amps to turn the engine over. The clicking could be coming from the starter bendix hitting the flywheel but not enough of cranking power to engage for engine start.

2. The starter solenoid is most likely the problem if it is clicking every time you turn the switch over. The battery sends power through this to engaged the starter which turns the flywheel. Sometimes these are located under the seating area, which can be a little hard to get to. Just follow the + cable from the battery and you will lead into it. God Luck and hope the $15 solenoid fixes the problem.

if the engine is a briggs and strattion the valves have to be re adj to 4-6 thou intake 5-7 on the exaust i am a sears teck i see that problem quite often