Woke up to two completely dead batteries. I believe the inside lights were left on by the last person who used it. When attempting to jump start them the van starts cranking with no keys in it. Any idea what is causing that. Thanks in advance.

 

Check the solenoid on the fender well or firewall (Usually on passenger side) for either sticking on or for something causing it to stay energized.Signal comes from the ign sw.
There is always the possibility the jumper positive cable was connected to the wrong side of the solenoid (The cable that goes directly to the starter.)