Odd experience: engine powered down going up hill, then almost stalled. PTO will not engage, now engine will not start or even turn over.

If your John Deere 4600 shuts off when put in gear, even after bypassing the seat switch, there could be several potential causes for this issue. Here are some troubleshooting steps you can take:

1. Check the Neutral Start Switch: The neutral start switch ensures that the tractor can only be started when it is in neutral. If this switch is malfunctioning, it may cause the engine to shut off when you engage a gear. Inspect the switch for any visible issues and consider testing or replacing it.
2. Inspect the PTO Switch: The power take-off (PTO) switch should be disengaged when shifting gears. A malfunctioning PTO switch could be causing the engine to shut down. Check the PTO switch for proper operation.
3. Examine Safety Interlock Switches: There are often multiple safety interlock switches on a tractor, including those associated with the brake, clutch, and other safety features. Check all safety interlock switches to ensure they are functioning correctly. A faulty safety switch could shut down the engine when a gear is engaged.
4. Battery Voltage and Connections: Low battery voltage or poor connections could lead to electrical issues. Check the battery voltage and ensure that the connections are clean and tight.
5. Inspect Fuses: Check the fuse box for any blown fuses. If a critical fuse is blown, it could lead to a shutdown when engaging gears.
6. Fuel System: Ensure that the fuel system is functioning properly. Check the fuel filter, fuel lines, and fuel supply to the engine. Lack of fuel flow could result in the engine shutting down.
7. Engine Sensors: Modern tractors are equipped with various sensors that contribute to engine control. A malfunctioning sensor, such as a crankshaft position sensor, could cause the engine to shut off unexpectedly.
8. Professional Inspection: If the issue persists after checking the above components, it may be advisable to seek professional assistance. A qualified mechanic or John Deere service technician can perform more in-depth diagnostics using specialized tools.

It's important to approach these troubleshooting steps carefully, and if you're uncertain or uncomfortable performing certain tasks, seek assistance from a professional. Additionally, refer to the tractor's manual for specific details about the safety interlock system and troubleshooting procedures.

It sounds like you have covered most of the possible issues with the electrical system. A ground issue could be a possibility, but there are other potential causes as well. Here are a few more things to check:

1. Check the wiring, connections, and terminals for the PTO. Verify that there are no loose or corroded connections and no damaged wiring.

2. Inspect the PTO clutch for wear, damage, or signs of shorting. A failing clutch can cause an increased electrical load, which can drain the battery and cause the engine to stall.

3. Check the belt tension and condition for the mower deck. A loose or worn belt can cause excessive load on the PTO and engine, leading to stalling.

Have a diagnostic test done as a guildline. To me it sounds like it could possibly be the water temperature sensor

May just need adjusted.

This is normal if you are going up hill but if you go down hill there should be very little work for the engine and transmission to do.
Going up hill as the engine starts to pull it is normal to kick into a lower gear to give the car more pulling power. If it does it in the down hill mode you should get it checked like low fluid or something.

possible cat converter

There is no problem with the revs going to 3 or 6. The revs need to climb so you have enough power to climb the hill (if the car upshifts under heavy load it may stall). But are you saying that the only way you can get it to shift out of first is to turn off the car? if so, then that is obviously not supposed to happen. It should shift shortly after you start driving down hill.

Any engine light? Can you hear the fuel pump run for a couple seconds when you turn the key to ON?

Your only out of ideas because you don't have
vehicle knowledge & experience

I would suggest you go for a ride at a repair shop
with a mechanic & a scanner on the car & then have
them do some testing

check the bellow on the throttlebody it is probibly cracked they dryrot