radio, front blower , rear blower ,automatic shut down, key chime does not work with th car running. But, with the car not runnig in the on position all the above work.

The only difference between the engine running and not running is the voltage at the battery. That fact should be no help with your problem.

Diodes in the alternator?

The battery light would be on if the engine was running and alternator not charging. Good thought.

We had a similar problem with one of my customers vans.It drove us crazy! At the lower left of the vehicle(remove splash guard) There is a BCM.Look for any corroded wires,and repair as needed.