TRANSFER CASE 1982 JEEP CJ7 WON'T SHIFT INTO 4 LOW

SOURCE: shift pattern for transfer case 1985 cj7

it matters what kind of transmission you have. my 85 jeep cj7 has stock dana 300 tranfer case. the pattern goes like this

4L
N
2H
4H

SOURCE: Jeep grand cherokee 247 Transfer case Interchange ?

if the shifter is the same and they have the same front driveshaft then yes

SOURCE: 1986 jeep cj7 4 cylinder engine timing

As far as I know, timing is "fixed" and cannot be adjusted on that one. To verify see if your distributor has an integral holddown not a seperate piece as you would find on an adjustable one.

SOURCE: Transfer case pops out of 4-lo

Either your linkage is not properly adjusted or the shift fork is a bit worn inside the transfer case. I have a bit of wear on my own and shift into low range while rolling with no load, between 5&20mph and it works fine except that I need to anticipate needing it before hand. One important rule...If it grinds, don't force it into gear. That will cause damage.
Also, if you just got it, change the oil in there...you have no idea when it was last serviced.

SOURCE: jeep stuck in 4 wd and transfer case shifter moves about freely

OK, simple problem, and a quick fix...  (And I consider changing my own oil to be the extent of my automotive education.)  I had this happen today.  A little online research from the jeep community showed me the external cable that connects your 4WD knob with the arm on the transfer case is held on that arm with a plastic clip that is fond of disappearing.  
When the jeep cooled down, I crawled under, found the cable end hanging freely, and simply set it back on the arm.  With no clip it will pop off again, but it allowed me to shift back to 2WD and roll home.  I understand a zip tie will keep it in place until you get a 3/16 nut of some sort.  (Can't be more specific about the nut yet, I'm waiting for more info.)  
It was a relief to find out that I didn't need to have anything done with the transfer case, etc...  If you show the dealer the problem, I'm told they often want to replace the whole cable, as the clip comes as part of the whole.  Waste of time and $$$, and I canceled the appointment with the dealership when I learned the simplicity of the problem.