15.5 hp Briggs and Stratton Bolen riding lawnmower model 13am762f765 wiil not crank. Battery is charged. Starter will turn fly wheel when jumped by 12v battery. Wjen key ois turned to start nothing. Not even a click from fuel solenoid.

Check voltage in battery.
If okay , could be solenoid .or safety switches
Check connections on battery,see if your getting power to solenoid.
Then check and see if your getting power to solenoid wire when key is turned.
Luck

Thanks DG, have to go get batteries for my VM, there dead as the mower. Was wondering about valve adjustment too. Before it would not start, I had it running, mowed the yard, next day it would not start. Cranked like an old model T. Barely cranked at all. Battery tender says battery is fully charged. Solenoid used to click now nothing. I'm thinking key switch. But will have to check all switchs with VM.

I am with DG on the solenoid, start there and then if proved we can check the several safety switches later.

Don't assume the battery is good unless its load tested and passes. Most auto parts stores will do that free of charge. Lawn tractor batteries tend to be crappy in quality.