5420 won't turn over

[Tucker2056]

I have a 2003 5420 that refuses to turn over. I've cleaned the battery terminals. I'ver check all the fuses and relays in the fuse box. The key switch checks out.
The saftey switches all have contenuity through them. I'm getting power the to pto lever safety switch but the seat switch and the neutral safety swith have no power runnin to them. Anyone give me an Idea of what I need to check before I pull the operator platform off and start check wires under there? Anything would be a help at this point thanks for your

 

[JD5210]

I have attached start system picture for the 5X10 which should be like the 5X20. On the 5x10 the seat switch does NOT play a role in starting. Based on the picture and what you said, I would check the wiring between the PTO switch and the neutral start switch.