Go back to the root cause: The DSP amp will shut itself off if it does not see either the DSP controller (separate controller, nav computer, or MID, depending on the car's configuration) or the radio over the car's I-Bus. This can be for several reasons:

1) Radio module disconnected
2) Nav computer disconnected or faulty
3) I-Bus fault
4) Amp coded for non-nav in a car with nav or TV (or vise versa)
5) Low battery that degrades module performance and causes unrelated symptoms
6) Internal module fault that affects I-bus communications

Since the screen works, your radio station changes, and volume works, etc. you can rule out any major module failures like #1, #2, or #3. Since this is the only symptom you mention on the I-Bus, you can probably also rule out a general I-Bus fault like #4. You say your battery is new, so that potentially rules out #5.

That leaves an internal fault in a component that allows all other functions to work but I-Bus communications related to component presence (#6). This is a very low probability, so I would go back to #4 or #5 as more likely.

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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