Well, the van is 14 years old and, to be fair, you did have it off the road with no gasoline conditioner or other precautions for two months, so it is bound to have more than a few hiccups up its sleeve. In this case, though, it is obvious that there is something going on so you need a place to start looking. In this case, it might be a good idea to look at the differential.
You indicated that you found a replacement transmission and, assuming you just had it swapped in, and had things buttoned up again — after performing the various steps you have to take — and, with that all done, you turned the key, it may very well be that the splined end of the transmission output shaft and the existing differential are just not meshing.
It is very possible that when you pulled out the first transmission that the relationship that existed between the former transmission and your van’s differential ended and that any new transmission might just not work, in the long run, with the existing differential.
No, this isn’t the way it is supposed to work as “interchangeable parts” are supposed to be “interchangeable,” meaning that every part is supposed to work with other parts, no matter when or where they are put together. However, the truth of the matter is that many times parts “learn” to live with other parts in a vehicle (it’s like a marriage, you learn to live together) so that everyone is just happy working with the part it has had working with it for some years.
When you break up the relationships that existed then vans and things tend to be unhappy and then they don’t work correctly.
With that said, look at the differential and be sure that the driveshaft and half-shafts are also true. If they are slipping out and not working then your van won’t run correctly no matter how many transmissions you drop in.