IF the solenoid is clicking, you don't have a safety switch issue.

Check ALL the battery connections including grounds. This includes engine mounting bolts to the frame.

Another possibility is a bad solenoid.
Jump across the 2 large studs. IF it cranks, the solenoid is bad.

BTW- 536.720112 does not come up on the Sears website.

robert - might consider removing that new battery again and taking it to a different shop that can LOAD test it...if such test was not performed in front of you last time.
A percentage of small batteries for riding mowers are defective from the gitgo - always wise to have them LOAD tested even as you purchase them. Such a battery will hold a surface charge, but won't start squat.
Also make sure your battery cable connection surfaces are cleaned to bright metal with sandpaper before being connected...

Thanks Bill
I'll have to put it back on and try that
I was told by the guy at the lawn mower shop that it is not being energized and that's why he thinks it's a safety switch or key switch and I have a Battery charger that reads 100% at 13.1 so I don't think it could be the battery
When I turned the key before I took the solenoid of if I did so a couple time the + wire from the battery to the solenoid got hot. I know I must sound stupid and I'm sure it's an easy thing to fix but electrical issues are just not my thing LOL

8 penlight batteries will generate 12V, but not have the capacity to crank your engine!

You might remove the spark plug (ground the lead) and see if the engine cranks.
There is a possibility the carb is leaking through and hydrolocked the cylinder.
Pull the dipstick and smell the oil for the presence of gasoline.

Hi Bill I rebuilt the carb a month ago and ride and have owned something like 17 M/C's and 11 quads over the years so carbs are like second nature to me and there is no gas in the oil I tried laying a screw driver over both the big post and nothing but sparks then tried contact on the + post and the small post orange wire post to the solenoid and it clicked with the key all the way over into the starting position with the clutch/brake all the way ingaged and locked so I guess the lawn mower shop was telling me the truth. So how can I check the safety switches and key switch? and how many safety switches would there be on this model?
Just want to thank everyone again for your time and all your comments
Rob

Did it crank with the spark plug removed?

AGAIN- If the solenoid clicks with the key switch, it's NOT a key switch or safety switch issue! IF it was, it WOULDN'T click.

What are the results of the battery LOAD TEST.

OR you can just wander down your own path......

Your Sears number doesn't come up. Are you sure it's correct?

Bill this is the model# 536.270112 manufacture date is 01092 will this help you help me? and it has a tecuseh motor 10 hp

How can I help you when you don't answer any questions?

The model DID come up at Sears when I tried again.