Determing if my 4x4 is working or not
 

What transfer case do you have? I am assuming an np242 since it has 2wd and the np231 wasn't offered in the grand Cherokee . What you have described is pretty normal for a np242, when I get into a situation where the rear is spinning I put it in 4x4 then put it in reverse for a few feet to get it to engage then it works fine.

Shifting the NP/NV242J Selec-Trac Transfer Case

2WD Position
This position is for driving on hard-surfaced roads under normal driving conditions when 4-wheel drive is not desired.

4x4 PART TIME Position
This position is designed for temporary use of 4-wheel drive when on-or off-road conditions such as deep snow or heavy ice require increased traction. When engaged, both the front and the rear axles are mechanically locked together and turn at the same speed. Do not use 4x4 PART TIME on dry, paved roads.

To engage, shift transfer case from 2WD to 4x4 PART TIME while the vehicle is moving at any legal speed.

An amber PART TIME lamp will illuminate on the instrument cluster when 4x4 PART TIME is selected.

4x4 FULL TIME Position
This is the primary 4-wheel drive position, which offers better traction when roads are wet, snow covered or icy. When engaged, the front and rear wheels axles are permitted to turn at different speeds to enhance maneuverability. Use 4x4 FULL TIME year-round on all road surfaces if you wish.

To engage, shift transfer case from 2WD to 4x4 FULL TIME while the vehicle is moving at any legal speed. When shifting, do it in a swift and firm movement.

When shifting from 2WD through 4x4 PART TIME to 4x4 FULL TIME, two momentary releases of the accelerator may be required after shifting.

A green FULL TIME lamp will illuminate on the instrument cluster when 4x4 FULL TIME is selected.

4 LO Position
This position is designed for temporary use of 4-wheel drive when off-road conditions require added low speed pulling power. Do not use 4 LO on dry, paved roads.

To engage, slow the vehicle to 2-3 mph (3-5 km/h), shift the transmission into Neutral (N), then shift the transfer case lever to Neutral, then to the right and pull firmly rearward to 4 LO.

Never attempt to engage Low Range when the vehicle is moving faster than 2-3 mph (3-5 km/h). Transfer case damage may result.

An amber PART TIME lamp will illuminate on the instrument cluster when 4 LO is selected.

When you are stuck with the rear wheels spinning the vehicle is not moving, that's why shifting into reverse and backing up a few feet helps it engage.

Just put it in beforehand.