Looks like this is yet to be resolved
So we might start again
If you read the snapper model number correctly then the wiring diagram should be as under
View attachment 63064
So when you turn the key to start battery power should go from the S terminal on the switch via the blue wire to trigger the solenoid
Because electricity has to make a full loop the solenoid trigger makes a ground contact to the frame.
When this happens the solenoid connects the heavy red & black cables on the solenoid to send high current to the starter to turn it .
Normally that blue wire would go through a couple of switches to prevent the engine cranking if the blades are engaged , brake is not on, drive is not in neutral.
But according to this diagram, it is a direct connection
Taking a step back the battery power to the B terminal on the key switch comes from the battery via the solenoid, through a fuse.
A common mistake is to put the mower power feed on the switched terminal on the solenoid ( the heavy cable that goes to the starter motor )
So for a no crank situation you need to check for voltage from the battery + to the solenoid , to the fuse, to the B terminal to the S terminal ( when key is in start position ) to the trigger terminal ( blue wire ) on the solenoid .
To double check the solenoid run a jumper from the red CABLE to the terminal the blue wire is on
Engine should crank
If not check the body of the solenoid is ground
Now for the fun bit, the no start
The black (ignition ground =kill ) wire can go to ground 3 ways
1) direct connection to ground via the key switch ( M + G )
The following assumes the T shaped outlines are supposed to be wire plugs
2) via the seat switch and pedal switch.
Note if the plug on the seat switch is disconnected or not fully connected that counts as no one in the seat
3) via the PTO switch Pedal switch & module ( can't really see what the module does unless it also turns the blades off .