Most of the time when this happens the problem is in the saftey switch on the brake/clutch peddal or the one on the mower engagement.
Sometimes the switches are bad and sometimes the switch actuator is not pressing the switch all the way down. The seat switch doesn't have anything to do with the engine turning over.
If this doesn't help you, feel free to contact me here at this question and I will try again.
In the start position, they are closed. because they have to complete the circuit.
I don't remember if you have an electric PTO clutch or a manual blade engagement. Be carefull if you have the Electric pto. You don't want to short out something. Best just to replace that swtch.
You will be able to do that on the brak/clutch switch, but NOT on the Electric PTO switch. Do the one on the brake switch first. If that doesn't work, you may have to replace the PTO switch...or at least take the switch in to the dealer for them to test.
I just received some new information from another expert that knows this specific model. Here is what he said.
This tractor has a complex circuit board as part of the ignition switch wiring. They are about $80.00. Our only diagnostic option is to replace it with a known good unit or hook it up to a computer Deere provides for this situation. The switch/module has pto, battery sensors, RIO all mounted to the circuit board. The most common failure is the brake lock lever spring breacs and the back side shorts out the back of the circuit board.