Well no wonder it did not go.
There should be a blue wire and a black wire that goes from the PTO switch to the clutch.
Where they go through the mower floor there should be 2 wire plug so you can change the clutch.
The starter solenoid and the PTO clutch can not be on the same circuit because they are mutually exclusive.
You can not start the mower with the blades engagd and the blades can not engage while you are starting the mower.
Now this is going to be a PIB type job but as some one has been in there making a mess out of things you now have to set it right.
Nice thing about JD is their wiring colour scheme is farily well consistant.
We will start everything from the key ( start ) switch because this will keep things simple as possible.
Remove the plate with the start switch & pto switch on it, it should have enough cable to pull up clear of the fender.
Flip it over and test for 12 V at the red wire and ground on the black wire.
If you do not have 12V at the red wire , nothing will work
Look closely at the back of the switch you will see the following
G - Ground wire,Black direct contact to ground
M - Magneto kill wire , White can be single double or tripple , connects to the magneto and the safety cut out switches. Kills the spart to turn off the engine , connects to the black wire with the ignition off.
B - Battery wire, Red, 12V connects to the + on the battery or the battery lead on the solenoid. This wire should have the fuse on it.
A - Accesory ( run) wire, Yellow , goes to the carb solenoid ( if you have one ) and the light switch ( if you have one )
S - Start wire , purple, usually goes to the PTO switch and becomes purple + white ( or + yellow ) then goes to the brake or neutral switch and becomes full purple again hence on to the starter solenoid.
Connections go like this
OFF G + M
ON B + A
START B + A + S
So check the ignition switch and report back
If your brain is not fried you can try tracing the purple wire. It may got to a few other things and usually will change colour every time it goes through a switch so purple + white, purple + yellow , purple + black etc etc etc.
Even worse it can go purple then purple + trace then revert to purple then purple + trace so just because a purple goes in and a purple come out it does not mean it has not been through a few switches.