Iin the back of your operators manual will be the circuit diagram for your mower.
Pull the plug out from the key switch and jump the B & I terminals together using a bare wire
Run another jumper from this bare wire to the S terminal
Every time you touch it the starter should crank.
If this happens then the key switch is suspect
If not then one of the safeties or the brake module is at fault.
I generally jump each switch one at a time to find the culprit .