...Bottom line being, it starts fine when cold, (computer has different instructions when cold) and runs fine there after.....
Ummm, sorta true, when the motor is cold the computer operates in open loop, all it does is ignore the O2 sensor feedback. It will also set a much richer A/F ratio, which is needed for a cold motor until it warms up. The O2 sensor is ignored for two reasons, 1. its NOT accurate at all until it gets warm, 2. its only useful for indicating stoichiometric A/F ratio, which you need richer than stoichiometric during warm up.
...Switching the HVAC on causes the computer to "reboot" there by killing the engine. When the wrong computer is installed, it starts every time, and the heat and ac work on all settings, it just runs really bad until about 50 or 55 miles per hour.
From your video, it appears the whole cars reboots, be careful NOT to confuse cause and effect. Shorts in the wire harness that connects to the PCM often blows the fuse (in most Chrylser's the PCM and Fuel Pump share a fuse and its labeled Fuel Pump), but a short can kill the PCM and make it reboot. If the electric system suffers some huge disruption it can kill everything in the car, including the PCM and cause the PCM to reboot.
That doesn't mean a PCM is rebooting all on its own, there is no easter egg programmed into PCM's that when you turn a knob it makes it reboot itself, there has to be some problem with the vehicle that causes the PCM to reboot.
...He guessed, and I might be inclined to believe this to be correct, that at about 50-55 the engine is warm and the computer believes that the tranny is in overdrive and kind of relaxes on trying to shift gears. I think I'm going to keep calling some junk yards and see what I can find as far as computers go. The stealership said that they were supprised the Jeep even starts with the wrong computer as they are VIN specific. I have a local junk yard searching for me, they said if they can find one they can get it via the parts exchange program and even have it "flashed" and warrenty it for 30 days if it does not just "plug-n-play. I told them to look, at this point, it is about the only thing that I have not tested. 50 bucks and at least I will know for sure.
This would NOT be the first dealership that has no idea what they're talking about, but they may be correct.
What is this "wrong computer", as in what vehicle is intended for?
PCM's being VIN specific can mean two things.
All PCM's are Part Number specific, manufacturers use the same "hardware" PCM in dozen of different vehicles, but the same PCM has different programming specific NOT only to the vehicle, but the options for that vehicle, and it changed from year to year as well. So, a part number is assigned and affixed with a sticker for each PCM according to the software loaded in it. So you can have two identical PCM's but they will have different part numbers because they have different software loaded into them, and that assures you get the right PCM with the Right Software for your vehicle. (Yes, the flashing goes off part number, the tools that do the flashing have that built in, so even the dealer can't flash the PCM with software for a different vehicle or different options, either intentionally or by mistake). All the Manufacturers/Dealerships have gone to VIN tracking of their vehicles, if you want to order a part you give them the VIN and they check a database to tell you the exact replacement part number you need (the database has all the info from the factory when your vehicle was put together). If this is what the dealer was thinking when he said VIN specific, he was correct, although he could have explained it better and that you could find what you're looking for by part number.
PCM's have the VIN programmed into them, but depending on the vehicle and its options, that may or may NOT make any difference at all. Most XJ's, if NOT all, if you have the wrong or NO VIN number programmed into it, it won't effect anything at all.
Later vehicles have anti-theft measures added into the electronics, things like immobilizers, etc. The electronics in the vehicle will compare VIN's programmed in the different electronic modules, including the PCM, and will NOT let the vehicle start if VIN's do NOT match (i.e. you can't get around the immobilizer to steal a car by swapping in different PCM). I really doubt any XJ's got this feature, it was only on the most expensive Chrysler vehicles when the XJ had finished it production run, but I could be wrong. Today its on even the cheapest economy cars. If this was what the dealer was talking about when he says its VIN specific, he's dead wrong and an idiot.
Any old PCM, the connectors might NOT even connect up to it. So you at least have got a similar PCM to connect the connectors. The pin-outs for the vehicle and PCM change, so you may entire circuits disconnected from the PCM. The PCM can have programming for different engines/transmissions.
So if you put in a PCM from another vehicle, that is NOT the specific part number for the PCM you're replacing, you are lucky it even ran. The problems you encounter from this new PCM are likely all rooted in the fact that NOT all the circuits are connected to the PCM and this PCM is programmed for another vehicle and engine, it is incorrectly controlling your vehicle and engine. Perhaps the circuits for the environmental control are NOT connected to this PCM, that is why it doesn't die, and the problem won't be fixed to find and fix the circuit problems in the environmental controls.