04 Wrangler AC fan only works on high speed (position4).

Take it to a qualified repair shop that has diagnostic information (shop manual ) An has a professional scan tool . Changed what sensor ? Coolant temp ? You don't guess an just replace parts . Doing a full vehicle scan ,checking for DTC'S in all the modules on the vehicle.

ENGINE HOT A/C OFF
Refer to Cooling System Description and Operation
Do the radiator cooling fans work ?
The engine cooling fan system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a Series/Parallel configuration that allows the engine control module (ECM) to operate both fans together at low or high speeds. The cooling fans receive positive voltage from the cooling fan relays which receive battery positive voltage from the underhood fuse block.
During low speed operation, the ECM supplies the ground path for the low speed fan relay, which is Fan 1 Relay, through the low speed cooling fan relay control circuit. This energizes the low speed fan relay coil, closes the relay contacts, and supplies battery positive voltage from the Fan 1 Fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the Series/Parallel relay, which is Fan 2 Relay, and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation, the ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. The ECM grounds the high speed fan relay, which is Fan 3 Relay and the Series/Parallel relay through the high speed cooling fan relay control circuit. This energizes the Series/Parallel relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the high speed fan relay coil is energized, the relay contacts close to provide battery positive voltage from the Fan 2 Fuse on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have their own ground path. The result is a parallel circuit with both fans running at high speed.
When the requests for fan activation is withdrawn, the fan may not turn OFF until the ignition switch is moved to the OFF position or the vehicle speed exceeds approximately 10 mph. This is to prevent a fan from cycling ON and OFF excessively at idle

DTC P1258: Engine Coolant Overtemperature - Protection Mode Active

Most fan and Ac relays are located in the under hood fuse and relay box. Adequately marked in owners manual or on plastic cover

There's a 10amp fuse that powers the ac clutch relay and compressor. There are 15amp fuses that power the blower motor and the ac control switch. All of those fuses get power from the key switch. The resistor and fan switch provide the ground circuit for the blower motor.
I would want to know if those fuses are getting power, and if the control panel is working. You should be able to ground the blower motor and make it run on high, and that should not have any effect on if the ac compressor is running or not.
It could be a key switch problem in that the circuit is not strong enough to handle the load from the blower and the compressor at the same time.

you have a bad blower resistor

you probably need new control switch.

it is the blower motor resistor. I do not know off of the top of my head if it is part of the climate control unit or external for your particular vehicle. However the symptoms match.

Yes I would go with the switch, BUT, does it have a resistor bank? That is, how does it reduce the speed? Many systems use resistors to lower the speed. Burnt or bad connections can cause this as well.
You can test the blower motor by connecting direct power from a source like the cigarette lighter if you are handy.
Most of the time the lower speeds konk out but the high speed continues to work this is the resistor bank that goes out.

Sounds like you may have a bad blower motor resistor.  When they go bad, they usually wipe out all speeds except high.  But could knock out just one or two of the speeds.  It should be located near the blower motor.

You'll have to go to the dealer and buy a new switch panel. There is a circuit board behind the switch panel that went bad on yours. Don't get one from the wrecking yard, I made that mistake once.

there is a blower resistor located near blower motor and housing under glove box area it is one connector with about 5 wires to it and looks thin, held by two screws this resistor controls fan speeds - possibly it will look burned may even be hot to the touch so be carefully it is the most probable cause since you obviously have power to it and ground only being the fan speeds the problem.