Odds are, you have the MKIII navigation computer, and it died when the car lost power.

Yours is the CD-based nav computer right?

The CD-based MKIII nav computer has a design flaw in which it can fry if it loses power before it fully shuts itself down. This started when you first noticed some strange electrical issues, so my hunch is that a low battery killed your nav computer.

The radio shut-off is directly related to the nav computer. The DSP amp is programmed to expect control inputs from the nav computer. (The nav computer runs the entire A/V system). If the amp does not detect the nav computer on the car's network, it will shut itself off after a brief time.

I do not know of a way to fix the MKIII. Your best bet is a use replacement from somewhere like eBay or a trusted parts reseller. I would recommend an upgrade to the DVD-based MKIV computer. It does not have the failure weakness of the MKIII, and it has a number of other great features over the MKIII.

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SOLD
2000 E38 750iL Highline Edition, Upgraded with the lastest 2006 X5 Electronics
MKIV Navigation, 16:9 Display, Bluetooth, TV/Video with Backup Camera, Sirius, and Aux Input