I have a 2006 Jeep Liberty...The Part Time 4wd light is ON then goes OFF when I engage the 4wd....any ideas..?

Please follow the link and scrool down to the 3.7 https://www.autozone.com/repairguides/Liberty-Wrangler-2006-2007/Coolant-Temperature-Sensor/Removal-Installation/_/P-0996b43f8075ae3c#hd1-1-3

SENSOR IN THE TRANSFER CASE SENDS SIGNAL FOR LIGHT, LINKAGE IS PROBLY HITTING IT, SOMETIMES THE WIRING GETS LOOSE AND HANGS DOWN THEN THE LINKAGE STARTS HITTING IT AND RUBBS THROUGH THE WIRING, GET SOME BUT CONNECTOERS THE SEALING KIND AND REPAIR

Could be bad wheel speed sensor. You need someone with a code reader that reads ABS codes.

part time or awd ?
do no engage part time 4wd on dry pavement.!! only on ice or dirt.
do post what your tires are touching? dirt or pavement????????

if stuck in 4L , on dry pavement , pull over to side of road, dirt
then shift out. if no dirt anywhere? sand or gravel or grass.?
then jack up one wheel then deselect 4Low. back do 2WD
options for your car, (do post what you have)
qoute sales brochure:
Those going 4WD can enjoy the standard Command-Trac II, or opt for the Selec-Trac II, featuring full-time AWD, 4WD Lo and a rearward-biased torque split. (end quote)

how you drive both cars, varies greatly.
in your glove box is an operators guide , did you read that yet
under how to drive in 4wd or awd.??????????

service time, complex.

take it in
or read the FSM. on topic
or alldata.com
did you put it into 4wd on dry pavement.? bad. on part time.RTM.
try jacking up 1 wheel and cycle it to see if you can unlock it.
there are lots of 4wd checks.

dealer only ,newer model ,this vehicle uses encrypted software to make work that only the dealers can do

just a suggestion but I had this with another make fwd and I had to put inreverse and drive several hundred feet and tehn switch out while i was driving

I questioned the dealer about my 2005 because mine was disengaging what I thought to be rough compared to what I was used to. They told me that I should shift the vehicle into Neutral before shifting the selector. I have also found that shifting between Reverse and Drive a couple of times while stopped has helped as well. By doing these couple of things, I have had no trouble since. I hope this helps as it might at least be something to try.

i see this alot. you need a new T-case position sensor. it runs about 70 bucks at a dealer