After replacing the transmission solenoid pack, transmission is not shifting properly and codes P0736, P1603 and U0101

From the description you really need a dealer level scan tool to watch the various sensor signals on the transmission. The P0882 showed low power to the transmission control unit, which could be a wiring short, but it could also be a failed PCM. The P1603 and U0101 are codes relating to the transmission controller not being able to communicate with the PCM or internal faults of the PCM. So that also points to it either having no power or internal failure. The P0736 would make sense in that the transmission section of the PCM controls all of the shifting and gear changes using the pressure in the transmission. If it has a power issue or internal failure it would set codes like that. As to needing a dealer, not true, you just need a better shop that can actually do diagnostic work.
The other item is the leak into the connector, those can cause all kinds of issues because it will short wires that should never connect and send bad info or voltages into the PCM and cause it to fail.
I would check the powers and grounds for the PCM as Chrysler has had a lot of issues with both of those and either can cause problems. As it starts and runs, I suspect it is more on the ground side, all four of the transmission related grounds go to the same point as shown in the third image, those multi wire connections like to fail.

https://www.2carpros.com/articles/how-to-check-wiring

Hello again Mr. Steve. So here is where I am at. I didn't like the way the battery terminal looked so I changed it. So far, no communication codes. I checked the transmission fluid by the light of day and added some and now its smack dab in between the holes for hot when the car is warmed up. It went into drive, did not shut off, and actually went forward though the initial engagement was a little rough. The only thing right now is it is going throw that P0736 code again and it won't move in reverse. How could changing the solenoid pack cause this problem? Baffling to say the least, for me anyway. Do you have any suggestions? I feel like I am so close. I just hope this can be rectified without great difficulty. Thank you so much for your time and help.

Was the pack a new pack or used? Either way it could be a bad solenoid, or something got into the passages. I would start by checking the connectors pins over real well, it's possible that the one for reverse is loose or corroded and not making contact, or the one for the speed sensor has an issue and is not seeing the correct signal when it goes into reverse. Does it try to move at all in reverse? Even loading the engine would be a sign that it isn't fully internal, but if you can shift into reverse and nothing happens then I would check the wiring first, a somewhat easy test would be to use the autostick and shift it down to first gear, does it move then? The same solenoid controls both low and reverse, just applies a different clutch to give you reverse. So, if it starts out in first and shifts up through each gear manually the solenoid itself likely isn't the issue.

The pack is new. When I put it in reverse the first time after starting, I feel the kick of it engaging but after that it feels like it does when I put it in neutral if that makes sense. It just revs when I give it gas. Drive gives quite a kick too, but it will move. Maybe some old gasket got in. The entire gasket was welded to the transmission, and I did the best I could but, the whole procedure was literally a pain. No room to work. I have checked the circuits and connectors, but it won't hurt to doublecheck. I haven't done the autostick but will first thing in the morning. I did not change the fluid or filter and I regret that now. Do you think a flush would be beneficial? Listen, you have no idea how much I appreciate your guidance. Thank you seems so insignificant but thank you just the same.

That description sounds like the solenoid isn't working, the kick in drive could be that it isn't engaging low gear and instead is starting out in second gear. With the old pack you had the error, but it worked in all gears, correct? If so, I would take a meter and test the solenoids for resistance, that can be done from the wiring connector. Take a meter set to resistance and connect one terminal to pin 4 on the transmission connector, then measure the resistance between it and pins 4, 5, 6 and 7 in turn. The readings at each one should be almost exactly the same. If that checks out, then it's likely that something got into the passage for reverse/low. If that is the case, then about the only way to get it out would be pulling the transmission pan and pulling the valve body apart to remove whatever is blocking the flow of fluid.
Removing it isn't really hard but it's messy.
First thing is to remove the battery and tray so you can get to the manual shift lever on the transmission. Make sure it is in low when you do that as it makes it easier.
Next you remove the pan and filter, next you remove the bolts that holt the valve body to the case. Now you need to grab the parking roller from the guide. Then remove the valve body. Tag the two accumulators that are in the case.
Before doing this though you need to be sure you have a scan tool available to do the relearn procedure. I might even try a relearn before you start pulling parts.

Mr. Steve, I did what you told me to no avail so I will check the resistance and see what's up. When I put the car on autostick the number 2 lit up. Should there not be a 1? It would not change either and I am under the impression that it can start out in third as well as second but please correct me if I am wrong. Now, about the relearn. I have little knowledge on that subject, (Actually, all these subjects.). I wasn't sure if my car needed it after the solenoid change, and honestly, I forgot to ask. Is this something any shop can do? I had no problems with my transmission itself, just the P0882 and as far as I can tell that is gone. I will let you know tomorrow what I find. You are turning into my favorite person real fast. Thank you!

It should go as low as one normally when it is selected manually. Relearn should be performed after most transmission repairs. You need a scan tool that can do bidirectional control to do it and that depends a lot on the shop's tools.

Mr. Steve, Hi.

Can you expand on what you mean by grabbing the parking roller from the guide? I had a stripped bolt, but I finally made it this far. It is going to start pouring rain of course, working on my car is the Western rain dance, but I am so close. Thanks

There is a roller that sets at the end of the park lever inside the transmission, image attached. You need to remove it to get the lever out and not let it fall into the case and cause problems.

Well, I am glad I was messing with the right thing, but how do you get the roller off? Was out there on the wet ground for hours. The car won that battle. Thanks

Transmission should be in low to get it loose, but it doesn't hurt to move the linkage to get it to drop free. I would be sure to put a big sheet under the car if you are doing this with the transmission in the car as the removal of the valve body will drop the check balls free and they love to hide. I would also suggest getting the one-year subscription to Alldata DIY for that vehicle, it has the full-service info for this procedure as well as showing where each ball goes. Runs about $20.00 but only covers one vehicle, you can print or same images in higher resolution as well.

Hello again, thanks for the check ball advice, it was a concern of mine not to mention I'm a Murphy's law kind of gal. I have the Mitchell's DIY, but couldn't find what I needed so I will indeed get the other manual. One last thing, I hope. Do you know where I might could get a replacement bolt for the stripped one? Been looking but I get different results daily and it gets confusing real fast. Thank you, thank you, thank you!

Hmm Mitchell should have the same info I posted above; they both mostly copy the OE information. We use both but I prefer Alldata as I'm used to using it, Mitchell tends to move things around, so it takes more to dig them out. Take a look under transmission, procedures, removing valve body. As for stripped bolts, best solution would be to use a Heli coil kit to repair threads and for replacement bolts I tend to hit you pull its or just order the bolts through a dealer if they are something odd. You might find some metric bolts in places like Lowes or a good hardware store or McMaster-Carr but they can take a while to find on their site.

Okay, my good man. I shall follow your advice and can't thank you enough for everything. Of course my rain dance worked all too well, but at first ray of sunshine I am going to get to it. With highest regards to you!

So, you're the one who is flooding my place huh, Thanks a lot. LOL. No rush, we'll be here, I know what it's like to have an open roof shop.

I did find what I need in the Mitchell so I might just swan dive on out to my car and try, try again. My luck there is an under toe.

Good luck, Take a snorkel and swim fins. Hopefully, whatever is blocking the flow will show up in one of the valves. Trying to get in deeper isn't fun. I think they do show the fluid paths on there as well so you might be able to use some air pressure on the passages to be sure they are clear.

You have no idea how many times I have said, "If this isn't it, I am done!". But seriously, if this isn't it, I will be needing a snorkel and fins for that creek I have been frequenting via my car no less. I should just get it over with and become a guide. Still having a heck of a time with this final task. I'm going to check it out with a camera and hopefully crack the code. These Pts are brutal! You are a port in this S#&% storm. Thank you

Hello Sir Steve, I have a question. So, When I took the cable off the manual lever and moved it to low, it was kind of a hard turn and skipped and clicked. I was under the car and had asked my husband to move it so I could better get to the rollers. When he did that, I could tell it moved a lot quicker and smoother. I wasn't sure how it was supposed to be but have since found out smooth and quick is the ticket. I am wondering if the problem could have caused it or if it caused the problem? Am I making sense, or have I finally lost it? Lol What are your thoughts?

As long as the lever moves it will shift, but it's possible that whatever is causing the fluid issue is in the main control spool that the lever moves. I'm hoping that you pull the VB off and find a piece of gasket material in one of the check balls or sticking a piston open or closed. Then you can reverse the process and have a working vehicle again. Just don't be like this person.