Welcome to JUST ANSWER small engines, let me try to help you !!
If you jump across the two large terminals on the starter solenoid #34, with old screwdrover does the engine spin? This checks the battery, cables and the starter.
You have seat switch and brake switch that can keep starter from engaging. Lock brake down, that eliminates the seat switch and try it.
The engine does spin and will start using the screwdriver. The brake switch does not eliminate the seat switch. The key seems to do nothing except turn the lights on and otherwise can be in the on position to start the engine with the screwdriver but does not stop the engine unless it is removed. So the ignition switch is faulty???
Have you checked the seat and brake switch for good connection? Not likely the key switch just wnet bad!
The brake switch is suspect as it does not cancel the seat switch. All runs well with the seat switch disconnected.
?? Runs well with seat switch disconnected?
Yes. I unplug a small black wire near the brake switch (wire is joined by two white plastic plugs) and that lets the motor run even if no weight on the seat AND allows going in reverse without cutting out motor.
but you can't start engine with key switch. So it appears the brake switch is the culpret.
That is my strongest suspicion. I will order a replacement. Thanks. I will give you a good rating.