Some suggestions
Does it actually go into 4x4 (e.g. light won't light when you push the button)? If not it could be the 4x4 motor problem (search the forums - you'll find the fix well documented, had to do it for my '92 ranger - worked great).
If it sort of goes into 4x4 (light goes on but doesn't get the additional traction of the front wheels), it could be front a wheel bearing / locking hub problem (the auto locking hubs are confusing - someone could have reassembled them incorrectly).
Also could be noise coming from the transfer case, transmission, etc. which mimics the 4x4 engagement sound - mine usually just sounds like a loud click / clunk.
You'll probably need to verify where the noise is coming from (e.g. have someone run alongside the truck while its making the noise) to try to identify the problem.
Oh, if it shudders when starting from a stop, while turning right or left, it could be a differential problem - that is also known and supposedly an easy fix but I don't know what it is. Forum search recommended.
BTW my experience is all with gen1 Explorers / Rangers (92 ranger, 94 explorer) and yours is a gen2 so YMMV re my comments above.