There is almost certainly water in the junction box behind the air filter. The connectors need to be opened, dried, corroded terminals fixed, and the source of water needs to be found and addressed. If the cover is installed wrong this can happen. Windshield gasket leaks are also likely. Pull up the passenger side carpet and see if the insulation layer is wet.
I've run into a very similar problem. With the truck running and foot on the brake the starter engages.