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I recently battled this one, even went so far as to replace the drive motor for the transfer case(old one was weak, but semi functional). I would start with draining the xfer case, put in fresh synthetic tranny fluid, 3 quarts will do it. Drive it for a week like that, then pull the electric motor off, put a 9/16 open end wrench on the stud sticking out, and work it back and forth through 2 hi/4 hi/4 low by hand about 50 times. After that, mine goes in and out of 4 lo smooth as glass now.
does the 4x4 light come on? I had similar problem and my transfer case plug with the 6 wires had 3 of the wires ripped out. I just took it off and had to make my own plug.
I had trouble with mine for awhile until I figured out that I had to push quite firmly on the brake pedal. Before that sometimes I would be pushing hard enough and others I wasn't so it seemed like an intermittent problem. Duh
That was when I first got it, you have probably had yours long enough that you have figured out the idiosyncricies.
Tap on the transfer case motor gently with a hammer. If it engages after that, plan on buying a replacement, corrosion has set in......
On another note, All owners with the ESOF 4wd should exercise all parts of the system at least once a month to keep everything lubed up and corrosion free. Engage 4wd hi, drive around the block. engage 4low. drive in your driveway back and forth 4 or 5 times. sitting in nuetral, go from 4lo to 4hi numerous times to break any corrosion and spread the internal grease around the motor and contacts. That should keep it in running shape for when you really need it this winter.