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How do I program an Analog Door Phone for an IP Office 406 to ring at all phones when Avaya DoorPhone button is pressed

Depends on the door phone. If it is acting like an extension you will need to add a user shortcode to make it autodial a hunt group.
Under the user short codes for the doorphone extension add SC:?D Feature:Dial Telephone #:(group ext number)

If the doorphone rings in on a trunk, then you would need to setup the correct incoming call route for it to ring where you want.