The bmw logo comes up and dims out continuously. I have no music 3 months now on 2004 BMW 545i

I won't say that I hate this car but something is always wrong, at the moment I have no music in the car for about 4 months now...When it's cold out, it would work as normal but when I switch off the car after reaching my destination, music shut down for good, just get the bmw logo and then it dims out and back on continuously till next morn (if it's cold out) I was told it's the radio, then another say battery, then another say it's another small box in the back under the spare tire, I just don't know what to think right now and I'm getting frustrated.

Asked by for the 2004 BMW 545i
seek insp and diag from a good german tech
These techs I'm taking my car to only specialize in bmw or audi, yet they're only saying they have to put it on the machine and run test to determine what the problem is...they're already talking about $100hr.. and stating that it takes about 6 hrs to diag the problem, you're talking about 6 bills and still no repair. radio alone cost $1100 plus and program...what's the point of wasting all that money just to find out a problem when I'm pretty sure there are a few ppl around that encountered this problem.
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Hi there, just wandering if you fixed the problem and what is it, I have my BMW 545 2005 for 6 years and lately experiencing the same problem, thank you