2002-2003 MY Gen3 Explorers used a Motorola 4x4 control module which was a stand alone controller behind the glovebox. For the 2004 MY the gen3 moved to CAN bus as method of controller communication and also got rid of the separate module moving it to instrument cluster and pcm embedded function. The move to CANbus allowed IVD to be possible and moved some sensors away from the transfer case as well.
The 4x4 control module was problematic and would cause a multitude of symptoms most frequently unannounced lack of 4x4 hi and low. Needless to say, the 4x4 CM looks for those speed sensors to determine front prop shaft speed, continuously comparing it to output shaft speed on tc, and rear diff speed sensor combined with throttle demand and engine load to use pwm actuation of the electromagnetic clutch on the output shaft to add power to front end. Switching to 4x4 hi applies pwm to 100% duty cycle with any throttle input, sometimes reducing pwm slightly with no throttle depending on calibration. Switching to 4x4 low causes shift fork to move range select internally to 4x4low, pwm duty cycle stays 100%.
The reason the 4L does not have the same sensors is the move to IVD which is traction control moved transfer case speed sensors to individual speed sensor or tone rings at the axleshafts in addition to the removal of the VSS in the rear diff. IVD became an option for 2004 model year. Your original case is a 1L which is a 2001 year design vs 4L which is a 2004 engineering number.
As for the symptoms, the transfer case may not be completely shot. The clutches internally have some friction/drag all the time, so removing shafts and turning front and rear outputs will make it seem like it is locked in 4x4. These torque on demand systems are quite different from older transfer cases which completely disengage front shaft in 2hi.
As above, the shift motor only controls internal reduction. It has nothing to do with 2hi to 4hi selection. I had seen some issues with shift fork pad wear on range select causes no 4x4low or stuck in 4x4low but it sounds like you are in hi range. I had also seen early builds with chain stretch excessive enough to cause the chain to jump cogs on 4x4 turns but a new chain fixed this.
There was an FSM or field service message and correpsonding TSB or technical service bulletin way back with a 4x4 system reflash due to complaints of 4x4 hi kicking in on slow speed tight turns due to the computer calibration reading tight turns as a demand for 4x4 hi but the affected units were IVD equipped. 4x4 was kicking in because the significantly increased granularity of individual wheel speeds and system sensitivity compared to the pre CAN bus systems. Remember, 4 wheel end speeds vs front shaft speed, output and VSS before.
What symptoms make you believe you are stuck in 4x4 other than turning input and output?
Long reply but it is good to fully understand the system before jumping in and replacing a bunch of parts.