sounds like one of your safety switches is either not working right or is unplugged. They aren't that hard to find.
Could be ign switch, starter solenoid, or wires in between.
</font><font color="blue" class="small">( My BX22 will not start as if it is not in neutral, but it is.
Is there another switch ? )</font>
The only problem I have had with my BX23 was the neutral switch. I shortwired it just to make sure it was "the one" causing problems. Started right up afterwards. I went straight for this solution as I actually heard it break when moving the lever.
You might try to measure power to and from it with ignition on / when key is turned to a starting position. If only power in one cable, then problem found. If no power, then problem before this switch. Think it's the pto switch before the neutral switch?