Once again, that's great information and a fantastic piece of diagnostics on your part!
That strongly implies that the WIN is either physically limited in travel -- can't turn to the START position -- or it's just plain got internal issues. Either way, a new WIN should get you back on the road and at least with that great piece of insight you won't have to have it towed.
The WIN will have to be programmed first to the van once replaced, then all keys have to be reintroduced. THEN there's the tire pressure stuff, so it will need to see someone with the proper scan tool capability, even if it's not the dealer. For reasons not known, some existing keys may NOT program again, leaving you with dead keys that need to be replaced. It happens.
It appears that the reason you never set a code is because no breach of security ever happened. The WIN simply cannot or will not supply a START signal but would be happy to do so if given the chance. As far as the van knows, you're just sitting there listening to Led Zeppelin or something with the key on. It doesn't realize you want to go for a ride.
A new WIN is the fix.
Thanks for all your help,