My 96 Cherokee Sport with the ASIN automatic and the 4.0 is acting strange. When I come to a stop sign or traffic light on a level surface it goes into like a Neutral mode. If I let my foot off the brake the jeep does not crawl forward at all. It used to. When I start out from a stop the transmission seems to be in 2nd or 3rd gear and is acting like it's slipping. I won't do that because I feel it will burn it up.
Now if I come to a stop and manually put the trans into 1st, I have to hold my foot on the brake or it will creep forward. Starting out like this gives me a true first and second gear from a stop. I manually shift it up to D after I know it has gone through 1st and 2nd. It shifts into the higher gears just fine.
Does this indicate trans solenoid failures or maybe the TCM (transmission control module)??
I have done 2 extractions of fluid through the fill tube. Removed 5 quarts each time and replaced with new fluid. Put about 50 miles on it between extractions. I adjusted the Kick down cable correctly out at the throttle body.
Put a pressure gage on the trans. Your fsm has the values to check. You will definitely find an issue. Easy process. Check solenoid resistance also. ( your trans is dying)
I had this same problem with my 96, ended up being the ignition switch. There is a black flat five or six way connector, it has two large red 10ga wires at one end. I found these had melted and damaged the switch causing the TCM to lose power. I replaced the switch and was back up and running, may want to pull the cover off around the ignition switch and take a peek.
A bad #1 solenoid would cause your symptoms. Check their resistance. On a 96, I would expect the trans computer losing power would throw a check engine code.