I would check the fuse on that light if you are sure the bulb is good.
Re: Battery, replacing is a great idea. Auto Zone has one for the Box for about $65 plus core charge.
Yes, dealer can provide code for you in about 60 seconds.
I have never tried the extra power supply approach but I am always leary around Box electronics. Hate the whole power surge issue.
Best of luck with new car and welcome to our board.
