How do i troubleshoot my transfer case problems

SOURCE: 4wd problem jeep wrangler yj 1995

i just bought a used 97 CHEROKEE but i had the same problem, when i got to looking at it i found out the front driveshaft was shot, look at that, if its not it i would say its probably the transfer case especially with an older vehicle like that which is a very expenxive repair

SOURCE: 4 wheel drive problem on Jeep YJ

you can also check the 4 wheel drive vacuum switch on top of the transfer case...got mine for 10 bucks from parts store...fixed the problem

SOURCE: 1993 Jeep Grand Cherokee Laredo wont drive when put into gear

No, not with out a lot of work. Electronics are most likely different on the 2 also.

SOURCE: 4x4 transimission clunks when engaged?

When engaging the 4WD system, you are pulling the lever on the Transfer Case right? Not the transmission, it's a different gearbox.
There were several versions of transfer cases that used both full and part-time 4 wheel drive.
From your description this sounds like a part-time transfer case.
Going with that, it is somewhat normal to hear and feel a mild clunk when engaging 4WD high range, especially if you are at a complete stand-still or under full throttle.
Try engaging 4WD High while slowly rolling at idle - no throttle. It should pull in fairly smoothly.
Once 4WD is engaged it will literally LOCK the front and rear axles together. So do not do it on hard dry pavement.
These older style 4WD systems need a little "give" especially when turning. The engineers assume you are not engaging 4WD unless you are in a somewhat slippery scenario.
Many CV joints, axles, U-Joints, differentials, and transfer cases are damaged and broken by folks who don't understand this.
Reading the owners manual should provide a clearer description of what you've got.
Bear in mind that when you come out of 4WD it may not completely release, again due to hard pavement binding up the axles. You can try this: backing up 10-25 feet in a straight line, or getting one set of wheels on the shoulder or in some gravel. That should allow it to release the transfer case and go back to everyday 2WD high.
I hope this helps.
:)

SOURCE: 4 wheel drive doesnt work.

Has this Jeep been modified at all?
It sounds like the shifter cable was reinstalled backwards.
Specifically the 4-Low "Not Climbing Well". 4-Low should give you the best torque and hill climbing ability.
Do you feel any "Binding" in the steering wheel (difficult to turn)?
Remember a Jeep uses real driveshafts and differentials to give you 4WD - you cannot engage 4WD or 4-Low on dry hard surfaces. It needs a little bit of slip between the wheels for turns.
Check you're fluids too.