2005 Jeep Laredo stuck in 4x4 low

okay not one word what the tires of the car are rolling on
dirt or ice. or raw hard pavement
nor the exact control settings are set.

the jeeps have many 4wd options new, (I have 2020 here)and I have full factory service manuals on all GC. made. gen 1,2,3.
most have Three levels of 4WD.
2005 to 2010 same as mine.
came with 2 choices new of transfer cases not told by you at all.
lets do both and answer what THEY DO and DO NOT DO.
nv140
The NV140 Quadra-Trac I (no part time modes) and uses brakes top stop tire slip. (smart)
is a single-speed transfer case and it is used in the Quadra- Trac I Full-Time 4-Wheel Drive System. It
provides full-time 4-wheel drive. The transfer case operates with an open center differential dividing engine torque
nearly evenly with 48 percent of engine torque to the front axle and 52 percent of engine torque to the rear axle. SO NOT YOURS

yours is this, read the users guide on 4wd low limits.
nv 245 has ,Quadra-TracT II and Quadra-DriveT II systems.
4wd low and lockups up the center differential.
and is not for pavement. (lacking ICE covering)
4WD Low, which multiplies engine torque 2.72
times and locks the clutch pack for maximum traction at all times
key word LOCKS. this for offroad and or ice only.
not for pavement.
do not use Low. or any kind of part time 4 wd modes, on pavement free if ice. (no matter the car owned)
or you windup the axles and steering fights the driver.
and is very dangerous to do and makes ABS go nuts. etc.
read page 240 in your users guide.
240
The Quadra-Trac IItransfer
case provides three mode positions - four wheel drive
high range, neutral, and four wheel drive low range.
and
The 4 LOW position is intended for loose, slippery
road surfaces only. Driving in the 4 LOW position on dry
hard surfaced roads may cause increased tire wear and
damage to driveline components.>. bingo the D word,.


if stuck in 4low
move one or more tire to ice or dirt.
shift out of 4low to 4hi at dead crawl speed,the slower the better
not grinding teeth to deathh wins.

4low is for dirt
or stuck in a snow drift.
otherwise stay out of 4low

https://www.carmanual.org/jeep-owners-manuals/2005-jeep-grand-cherokee-owners-manual-2983/

SJ one of only 17,254 every built. rare it is.
1987 is First Chysler jeep.
are you on snow/ice, dirt?
we cant guess what you tires touch (we sure cant guess)
First learn how part time 4wd works.
this a SJ jeep right>?
the non grand ,version is PART TIME ONLY (ice or dirt never clean pavement)
my guess, is this is the
NP 228-229 box. transfer case. did you look>?


here is the list.
lots
http://jeep.wikia.com/wiki/List_of_Jeep_transfer_cases





the SP228/9 is full time only in 4wd high.
i low its part time
part time is for dirt or rock crawling.
or stuck in deep snow very very slow
or ice, if crazy using this gear on ice, it will slip bad.

why not tell the poster, what the tires are resting on
or where you are driving
on the pavement
or off road.

the rules for Part time are strick and if no followed,
you can damage the drive ling (chain in case)
or get in to an accident, and causes injuries.

move car to dirt or ice, gravel , off pavement
PT is not for pavement unless covered in ice.
the operators guide told you that.

move to dirt and shift out.
if you have not already damaged it.. that is.

how'd it get there?
driving on hard pavement will in fact get it stuck,
are you on ice or dirt. ?
if on pavement, it will stick on all part time 4wd cars.
its not AWD, so can not be driven on hard pavement.
only ice,snow, dirt.
if on hard pavement move to the dirt side of road and it will now release. this is called windup, and will damage the drive line.
if you keep doing this.

WHAT SURFACE are you driving on,...????? ICE , pavement?
part time, full time or AWD? which is it.
Autotack????
open diffs?
some AWD have a center diff, lock , is that on? (never on pavemnt)


a chevy Jeep Grand cherokee??????
is this a 4wd question?
are you driving on pavement , ICE, snow or dirt.
my wild guess, is this is Cebby. and is not a Jeep
and is PART TIME 4WD and is not AWD
if you drive on pavement that is not covered in ice or snow
that is wrong, the manual explains that.
part time 4wd only works on ice or dirt.
more simply,. 1 tire must slip, that is be on something like ICE or dirt .
Part time 4wd has no center differentail
and if you drive on pavement (dry) it will windup the drive line
and something breaks.
so REpost what you are driving on , the world is complex
dirt,sand,snow, granite, ice, mud, ?

im guessing, here is trac-lock. discussion....
http://www.fullsizechevy.com/forum/general-discussion/technical-maintenance/504267-2002-silverado-z71-4x4-not-working.html

here are the options, then
quote:
The only 4WD options were either the base option with a manual 4WD shifter in the floor OR the more expensive pushbutton version in the dash. The pushbutton version also provides full-time 4WD capability, called AutoTrac. Whether the rear differential is Limited Slip or not is a separate option. Limited Slip is not available in the front axle.
end quote.
the base version is not for Dry pavement, and if you make that
mistake, the gears will be very hard to impossible to UN SHIFT
due to driveline gross wind up, just like any jeep, 4wd.
RTM.

On these issue, there are few solved help links for troubleshooting the issue easily.-------

Click the link below: ---

No 4x4 light on dash?

http://repairhelpcenter.blogspot.com/2011/12/no-4x4-light-on-dash.html

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4X4 Truck makes roaring noise in the front end?

http://schematicsdiagram.blogspot.com/2012/01/4x4-truck-makes-roaring-noise-in-front.html

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Car will not go into 4WD high or 4WD low?

http://schematicsdiagram.blogspot.com/2011/12/car-will-not-go-into-4wd-high-or-4wd.html

--------------

No 4x4 light on dash?

http://repairhelpcenter.blogspot.com/2011/12/no-4x4-light-on-dash.html

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4 wheel drive system will not disengage?

http://technoanswers.blogspot.com/2012/01/4-wheel-drive-system-will-not-disengage.html

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4WD light is flashing and beeping? NO 4WD high?

http://schematicsdiagram.blogspot.in/2012/02/4wd-light-is-flashing-and-beeping-no.html

----------

2002 Jeep Wrangler: 4WD Idiot Light is ON?

http://technoanswers.blogspot.in/2012/06/2002-jeep-wrangler-4wd-idiot-light-is.html

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Traction control switch will not engage on 4WD High or Low

http://whoisbyme.blogspot.com/2012/10/traction-control-switch-will-not-engage.html

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4WD light flashing and 4WD will engage after few minutes

http://repairhelpcenter.blogspot.com/2012/10/4wd-light-flashing-and-4wd-will-engage.html

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2008 Toyota Tundra: 4x4 Wheel Drive Light is Flashing?

http://technoanswers.blogspot.in/2012/05/2008-toyota-tundra-4x4-wheel-drive.html

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4x4 front differential will not engage the axle on ford?

http://technoanswers.blogspot.in/2012/02/4x4-front-differential-will-not-engage.html

-------

4x4 will not engage on Ford F150?

http://technoanswers.blogspot.in/2012/02/4x4-will-not-engage-on-ford-f150.html

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Dodge Ram 4x4 light keeps flashing

4X4 LOW LIGHT IS FLASHING ON DASH

http://technoanswers.blogspot.in/2012/09/dodge-ram-4x4-light-keeps-flashing.html

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Ford 4x4 front wheels will not engage?

http://technoanswers.blogspot.in/2012/02/ford-4x4-front-wheels-will-not-engage.html

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These details will help.

Thanks.

This is normal for a 4X4 to do, 4WD on a Jeep with out a "full time mode" is only meant for wet and slippery conditions. Leaving it in 4WD on dry pavement can damage the drive line

Your jeep should have full time four wheel drive. To place the transfer case in low range look down to the console towards the rear and you will see a "T" shaped handle. To place it into low range you should stop place the vehicle into park and lift the T handle and in the dash a 4X4 indicator lamp will light up. The traction button on the dash would be used in 4 wheel high mode when you start to experience wheel slippage upon take off from a stopped position. This will give you a little more control. You only need to use the low range for very slow speeds in mud or snow. Otherwise just leave it in high range because it is always using 4 wheel drive. This is a very reliable system which Jeep has refined over the years. Your Grand Cherokee is not designed fro hard core off road use. Hard core off road use will destroy the undercarriage. The Grand Cherokee is more of a luxury soccer mom 4X4 with good road manners, a comfortable ride, and good reliability.

With the Jeep in park, move the left shifter to 4 wheel drive. Proceed to put right shifter into drive, proceed to drive. Only use 4wheel drive when neccessary...ie...snow, mud, use 4 wheel lo in steep incline or when really bogged down.

Hope this helps

like it says full time is all the time part time disengages the one differential for slightly better fuel milage at the expense of less off road capability