Kenmore Elite D/W 665.13963K015 beeps, flashes and then shuts off after closing door to start.

Are there any error codes in the display? Did you try unplugging it for a minute or so and replugging it to try and reset the electronics? By chance is it still under warranty either from the store or manufacturer?

Back to you.

The flashes are error codes. Pull the toe plate off and check to see if error codes are on there. Sometimes you can reset with pushing a series of buttons.