OK lets take things from the top, slowly
So you were trying to start the mower, it would rotate bet not fire.
You then disconnected the the magneto kill wire & the engine burst into life.
But if you reconnct the magneto kill wire the engine stops dead
And with the engine running if you try to turn on the blades they do nothing.
Is that what is happening because it does not make sense .
I don't have a wiring diagram for your specific mower so this will be very general.
JD like putting relays in their real ride ons and most are the simple 30 A headlamp ones .
So if that is your case, get a new one then swap them over 1 at a time.
Worst case is you end up with a good spare.
Now we look at the safety switches.
There are two different sets.
The PTO and parking brake will prevent the engine from cranking.
These are a daisy chain so power goes through the ignition switch, through the PTO switch to the starting solenoid.
The neutral switch, Brake switch , PTO switch, seat switch, reverse switch have ground circuits that will prevent the magneto from firing.
These switchs are wired in pairs , seat + brake , seat + pto, pto + reverse .
The PTO switch should energise the PTO clutch with the mower sitting still without the engine running.
So turn on the ignition , engage the PTO, you should be able to hear the clutch throw with a reasonable thud.
If so the PTO section of the PTO switch is working.
A 4 wire switch will have 2 sets of contacts 1 are normally open & the other are normally closed.
So make up a short patch lead, disconnect the plug at the back of these switches and jump the normally open side.
Try to run the mower.
If problem persists give the switch a good tub with WD 40, or similar and work the switch vigirously to clean out any dust & debris in the switch.
Hook it back up and move on to the next one.
Painfully slow & tedious
I don't have a wiring diagram for your specific mower so this will be very general.
JD like putting relays in their real ride ons and most are the simple 30 A headlamp ones .
So if that is your case, get a new one then swap them over 1 at a time.
Worst case is you end up with a good spare.
Now we look at the safety switches.
There are two different sets.
The PTO and parking brake will prevent the engine from cranking.
These are a daisy chain so power goes through the ignition switch, through the PTO switch to the starting solenoid.
The neutral switch, Brake switch , PTO switch, seat switch, reverse switch have ground circuits that will prevent the magneto from firing.
These switchs are wired in pairs , seat + brake , seat + pto, pto + reverse .
The PTO switch should energise the PTO clutch with the mower sitting still without the engine running.
So turn on the ignition , engage the PTO, you should be able to hear the clutch throw with a reasonable thud.
If so the PTO section of the PTO switch is working.
A 4 wire switch will have 2 sets of contacts 1 are normally open & the other are normally closed.
So make up a short patch lead, disconnect the plug at the back of these switches and jump the normally open side.
Try to run the mower.
If problem persists give the switch a good tub with WD 40, or similar and work the switch vigirously to clean out any dust & debris in the switch.
Hook it back up and move on to the next one.
Painfully slow & tedious