Oil change light will not go off

There is video on it

Noise doesn't have to come from transfer case

You have to find the noise

Transfer case fluid should have been changed along
with all fluids,years ago.

No Preventative Maintenance Plan there ?
No Log Book of what never gets done !!

you may have to use a scanner to reset the CPU for this unless there is something in the owners hand book on how to reset after a service.

Follow the procedure found here

https://resetoillight.com/lincoln/oil-change-light-reset-lincoln-town-car-2006-2007-2008-2009/

turn key on til message appears,push gas pedal to floor 3 times (engine not running)

The following procedure will reset your oil change light. Thank you for using Fixya!

2008-2010 Sable

1. Turn the ignition to run (one position before starting engine).
2. Press and release SETUP to display "OIL LIFE XXX% HOLD RESET = NEW".
3. Press and hold RESET for 2 seconds and release to reset the oil life to 100%.
4. Turn the ignition off and then start the engine to verify the indicator has been reset.

TRY RESETTING OIL CHANGELIGHT BY TURNING THE IGNITION SWITCH TO THE ON POSITION WITH ENGINE OFF.TURN IGNITION SWITCH ON 10 SECONDS PUMP ACCELRATOR SLOWLY 3 TIMES .UNTIL OIL CHANGE LIGHT FLASHES THEN IT HAS RESET.

Directions are in the book, but you would put the key in and turn it all the way, just don't start engine. Pump gas pedal all the way to the floor 3 times slowly, but it has to be with 10 seconds. Turn key off and when you start again, oil changed chime and warning should not be on. If it is, try again.

To reset your maintenance reminder system (even if the light hasn’t come on yet), you’ll need to turn your key to on (but don’t start!) and make sure your odometer is on TRIP A. Then key off. Press and hold the Odometer/Trip button. While holding down on the button, key the ignition to on (Don’t start the engine!) The display panel will count down from “------“ to “-“Continue pressing the button until the Trip A is displayed. After this step, you are done.

Turn key to the run posistion and pump the gas peadle 3 times under 5 seconds.

Press odometer reset/adjustment shaft in, hold in and turn key to run position. Keep holding in the reset shaft in for about 30 seconds. release shaft. turn key off. restart car. Service Light should go off in about 5 seconds.