Shutting off a fuel solenoid isn't going to kill the motor right away. Every ignition switch I've ever had to mess with kills the engine by causing a short to ground that shuts it off electrically. I can't say for certain that's your issue or that your machine even works that way but I would trace the wiring and look for a break somewhere. All that time sitting, I would bet that a mouse has chewed on at least some of the wiring so it should probably be gone through anyway. It might also be corrosion on the switch itself.