I think the switch for the hast pedal would keep it from starting if it thinks the pedal is pressed. It seems like what the op describes is the tractor is running, he presses the pedal, it dies.
Id have to see some kind of wiring diagram to understand what could be wrong. I assume you checked fuses. I still say it’s the seat safety switch, the pto or HST pedal switches would keep the tractor from starting.
Edit, I say the seat safety switch, but it could be somewhere down stream from the actual switch.