Most of the time when that kind of problem starts happening it due to
the    shift motor that's mounted on the transfer case.  I repaired
mine twice and last time I bought a new shift motor.  They aren't very
expensive, around $130.  Try www.Rockauto.com

Instructions:

From cputnam@mindspring.com Tues DEC 22 09:29:01 1998
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From: "Chris Putnam" <cputnam@mindspring.com>
Newsgroups: rec.autos.makers.ford.explorer
Subject: Re: 4wd not engaging
Date: Tue, 22 Dec 1998 11:29:01 -0500
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Tah dah!

It took a while, but I was able to remove the transfer case motor,
disassemble and clean the motor, reinstall, reset and it is working
better
than new.  Dr. Bob's and the other information on Jeff Singleton's
website
were excellent.

http://www.glue.umd.edu/~singletn/exp.html  (this website no longer
exists)

Admittedly, I didn't read all the info on Jeff's site, so I had to
fumble
through some of it (mainly the motor disassembly and shaft alignment)
on my
own.

Here's my additional info to the info I found there:
1) As several people stated, you do NOT have to drain the transfer
case
fluid to remove the motor.
2) The motor is MUCH easier to work on out from under the vehicle. The
only
trick is what to do with the permanent wire coming out of the transfer
case
into the wiring harness connector on the motor.  As another
contributer
offered, you can remove this wire (the center pin on my '93) by
removing the
lock from inside the connector.  I used a large paperclip,
straightened with
a very small bend (90 degrees, ~1 mm) on the end to hook beneath the
restraining plug to pull it out from amongst the pins.  This allows
the lock
on the center pin to be gently move to the side allowing the wire and
pin to
be pulled out from the back.  Fortunately, the other pins behaved and
stayed
in place during this procedure.  You could do the speed sensor wires
the
same way, but I just removed the speed sensor from the transfer case
and
took it with the wiring harness.
3) after reassembly and reinstallation, I reconnected the battery,
started
the engine and gave it a try.  Nothing...  I couldn't believe it since
I had
tested and heard the motor turn before putting it back on the shaft.
Out of
desperation, I went back and hit the reset button on the electronic
controller one last time.  The mysterious red light reappeared, but
this
hadn't made a difference before the motor was removed and cleaned.  I
tried
one last time and it worked!!!

~$300 saved and mechanical fulfillment at the same time!

Thanks, everyone.
-Chris