Hello, I'm Chris, a current Ford Lincoln Mercury employee.
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Try this and tell me the results if unsuccessful.
PLace the switch in 4 low and drive straight 10 feet. Now come to a stop and go to neutral and hold your foot on the brakes. Now shift to 4 high and wait. The dash should indicate 4 high and you should hear it shift.
OK try this. Start the vehicle and leave the 4x4 shifter in the lowest setting being 2wd or AWD. Now shift it to 4 high while in neutral and your foot on the brake, Does it indicate 4 high on the dash. If so go to 4 low and see if it indicates. If it does then try to go back out as previously stated.
If this fails then you will need to remove the shift motor from the transfer case and manually turn the transfer case shift lever to get out of low. Once out of low and the shift motor hanging you need to have someone work the switch inside the vehicle while in neutral and there foot on the brake. When they do this see if the shifter motor will move back and forth. If it does then install it on the transfer case while in 2wd since the transfer case has been manually shifted to 2wd. If it fails again or the motor does not move then a new shift motor is needed.
There is a slim possible concern that you damaged the shift fork or selector shaft inside the transfer case when you accidentally when to low. When manually shifting the transfer case have someone in the vehicle to apply the brakes or help roll the vehicle. You may need to roll the vehicle slightly to complete the shift and have them hold the brakes if needed since you can accidentally go to neutral in the transfer case allowing the vehicle to roll over you.