The problem is not the transmission; you or the previous owner may have disconnected the battery in the past causing loss of voltage to the vehicle electrical system.
The consequence is the 4 WD module to go to sleep permanently.
The module does not wake back up when power is restored.
The only way to restore normal 4WD is to replace the module with new one.
You will not have any problem with the transmission when the module is replaced.
When disconnecting the battery, make sure the plug in battery saver is in place. It keeps computer memory alive while battery is disconnected.
If fuse #8, 25 Amp, located in the fuse block-underhood is good, the problem is the module. If fuse is bad, replace it.