The automatic transmission you have is an electronically-controlled 4-speed (forward) automatic transmission. It is VERY sensitive to fluid type and viscosity (thickness). You MUST be using either ATF-3, ATF-4 or Chrysler 7176 fluid. Read all about it on allpar.com!
There is a "solenoid pack" bolted (with three bolts with head size 10mm) to the front of the transmission on the drivers side of the vehicle, down about shin level, under the air intake assembly (which you'll have to remove for easy access). It contains four electromagnetic solenoids that, when energized in in various combinations, choose which gear the transmission will be in. There is a large connector going into the top of the solenoid pack, held on by a single bolt in the middle (8mm head size I think). There have been six different versions of solenoid packs so far! The solenoids are "pulse width modulated" by the TCM (transmission control module) that is bolted to the passenger side inner fender. If the solenoid pack had an electrical problem, it could have damaged the TCM. Converesly, if the TCM had any kind of an electrical problem, it could have damaged the solenoid pack! So, you could replace either with a new one and then damage the new replacement in a flash! So replace BOTH AT THE SAME TIME, WITH NEW ONES! An example of bad parts damaging other parts would be this: Suppose you have a table lamp that doesn't work. You plug it in a known good socket and turn the switch, but there is no light. You test the light bulb with an ohmeter and it shows that the bulb is not "open" - that is, there is continuity. So you install a new switch, screw in your old light bulb, twist the switch and pow! Your new switch is toast! Why? You didn't know it, but your light bulb was not "open" but it was shorted That is how an old "bad" part can damage a new part!
Make absolutely sure you have a good ground strap going to the transmission case (the strap is near the starter)!There is another possibility, and that is a wire harness and/or connector problem. That is VERY likely if the wiring harness was under much strain while removing or installing the transmission! An electrical scan using a Chrysler DRB-III (DRB-3) scan tool will often pinpoint the exact problem(s) with A604 / 41TE transmissions, but those scanners are expensive and frequently "dealer only" equipment. Don't expect any help from a low-cost scanner such as Autozone will use on your vehicle for "free!" Good luck!