Rebel is a genius, or at least very experienced. A thorough cleaning of the battery cables got the car started (using a fob with no battery). So now the question is did the dying battery cause the windows to go down by themselves or did the window issue cause the battery to die?

I also have the airbag light on if you are aware of any known issues that can cause that.

That is why I said to take out the remote fob battery, and see how it does without it. I have personally seen 2 fobs printed circuit boards go bad and send screwy signals to the van to do such as you have happening. It is in other words a "test Trial". If no problems show up for a couple of days, put the fob battery back in and again see what happens.
There can be many causes of a particular problem, I am suggesting an easy way to check the situation out..And this is from first hand experience!
How old was the battery and how much preventive service has the van been given?
EDIT: the airbag light will need diagnostic scan with a scan tool that can read BCM codes, the key dance and regular OBD11 scanners can not access those. Bright side is the airbag codes are very specific as to what is wrong.
Good luck and will still keep an eye out for any updates.

Battery was 3.5 years old.

PM has mostly just been the basics such as oil changes. Spark plugs and coil pack has been replaced. I had to replace the heater hose Y fitting a while back which included changing the coolant.

A non-dealer shop looked at the airbag light and couldn't read it because they did not have the right scanner. They said take it to the dealer, so I guess I will have to do that.

That will cost you big time..Spend some phone time and call a couple reputable independant repair shops near you and ask if they have a scanner that can access the body and airbag modules for codes for your T&C.
Again from experience, I have found the clockspring assembly in the steering column to be a weak spot. BUT best to get the code(s) and know for sure.
EDIT: with the electronics in these vans that is a reasonable old age for lifespan, especially with the corrosion and electrical troubles you have had.

I know you have a busy schedule..But how are things going, Any updates?

The windows going down could be due to a bad contact in the key fob, if the unlock switch is making contact without pressing the button it could be activating the "Remote Open Window Feature"

That feature is listed in the owners manual index as "Express Down Windows"

Thanks for the "details" on this. All in all there is a problem in the remote as I stated. And I have seen them do more than activate express down functions. That is why I posted as I did to make sure that it was/was not a remote problem.

After replacing the battery and cleaning the terminals, everything appeared to be working fine. We went several days using "my" fob with no battery and we had no problems. Then we went several days using "her" fob with no problems. Until today when using her fob she had the windows go down and some issues with the blinkers and lights. I thought we were past this, but I guess not. The problem originally occurred using her fob, so it could still be a problem with her fob. I don't drive it enough to know if the problem happens with my fob. I have still never seen it happen and only have my wife's reports about it.

That is EXACTLY what I have seen and tied to fix...It is a bad FOB unit. You did not specifically say if the wife's fob had NO battery or if it did when this occurred.
Think of it this way...They work just like the buttons on a TV remote control, heavily used function buttons wear out and stop working or do strange actions. You are looking at either NO remote functions(NO battery) or buying new key/remote fobs and having them programmed to match your van.

Her fob still has battery in it. It happened with me driving today with my fob with battery and her fob with battery in my pocket.