4 wheel drive doesnt engage. When you move selector to 4 low, its in low but only drives rear wheels. Other selections show its in awd or 4 hi but same thing, only rear tires drive.

Not all cherokees were fitted with a 2 wheel drive option. You should have two shift sticks in the centre console. Your normal Park, Reverse and Drive selector and a smaller, shorter stick to the left of it.
This shorter stick will show you your drive options.
If you only have the first three listed yours is permanently 4 wheel drive, sometimes called AWD, (All Wheel Drive).
Starting furthest away from the engine, they should read as...
4Lo - Low ratio 4 wheel drive used just for 'off road' driving.
N - Neutral. This disconnects ALL drive to ALL the wheels.
4 FULL TIME - High Ratio 4 wheel drive. Normal road 4
wheel drive.
"Options that might not be fitted".
4 PART TIME - Automatically switches from 2 wheel drive
to 4 wheel drive if the rear wheels start to lose grip.
2WD - Dedicated 2 wheel drive only. Power is sent to the
rear wheels.

did you turn the locks on the wheels, or check the fuses

To understand you
the car runs but when you engage drive it doesn't move
however if you move the selector from 2 wheel drive to 4 wheel drive it does move
is that correct
logically if that is the case the auto transmission is working but the drive to the rear wheels is not functioning
That would point to a problem in the , diff connection ( broken rear axle )
by engaging 4 wheel drive you are moving by the front diff only

awd drive cars have a differential action between front and rear wheels and there should be a switch that allows you to lock up that action for adverse conditions
if the rear wheels are not working , it is because there is no drive action to the front wheels ( front wheels spinning or broken drive shaft to the front)
all wheel drive means that in normal driving when there is traction on all 4 wheels that the power is transmitted evenly to all 4 wheels
It is not 4 wheel drive where power is applied to both axles or in the event of one axle loosing traction the other axle still drives

Your DII is (always) in 4 wheel drive. There is NO 2x wheel drive option on a DII, it's always in 4x4 high, or low. To select 4-wheel drive low, put your transmission in neutral and pull down the high low gear selector.

The vehicle is always in AWD and that cannot be altered . There is a 3rd diff in the gear box that allows independent operation of the front and rear wheels to prevent drive line wind up . When you select 4WD you lock up that 3rd diff so that both front and rear axles have to turn. This results in drive line torque wind up so the vehicle must not be driven in this mode on hard surfaces as there is no means for the wheels to slip and relieve the torque wind up . To loose the wind up reverse for several yards and any actuators that are trying to move will be able to or drive on slippery surfaces to allow the wheels to slip

all wheel drive vehicles have to work at both ends all the time unless you have a major failure in the drive train. That is why it is called all wheel drive as opposed to 4 wheel drive. With 4 wheel drive you have the option of rear wheel drive or 4 wheel drive and normally in a high ratio or low ratio gear selection. With some all wheel drive vehicles there is a selector that locks the middle diff and creates a 4 wheel drive option without the high/low gear ratio option. So in practice if the both front wheels are in the bog then there is no all wheel drive as the centre diff is working as it should and placing all the action in the rear wheels which will not be turning as they have traction so the front wheels spin faster.. If you have a centre diff lock option ensure that it is operational.

it is most likely an automatic awd, 4 hi is full time 4 wheel drive, 4 lo is full time 4 wheel drive but at a very low gear ratio and should not exceed 25 mph or could cause damage. and DO NOT shift into 4 lo while vehicle is in motion. Auto is a 2 wheel drive but automatically engages into 4 wheel drive under heavy acceleration.

I assume that the vehicle has a rotating knob on the left side of the dash for four wheel drive. It may have been put into 4 low by mistake. To get it out, start the vehicle and put it in drive, select 4 low on the 4 wheel drive selector, take your foot off the brake and get the vehicle rolling at a walking pace (1-2 m.p.h.) then move the selector to 4 high, stop the vehicle and move selector to 2 high.

Awd is on demand 4wd, better fuel economy
4wd high is locked in high range
4wd low is lock in low range