Did you take the negative (ground) cable loose at the body/frame to check for a rusty/dirty/loose connection? That's always my first suspicion when a mower or car won't start. Also, most modern mowers have a 'safety switch' on the brake pedal. If that switch is worn, loose or has poor connections, you might not be getting continuous voltage to the starter solenoid.
Hope you find your solution soon!
Dave B.