first thing I did was hit CTRL-F and search for "battery" in the original post. '07 X5 likely needs a new battery by now (and go from there).

I do wonder why it doesn't show the battery icon on the dash as it did with mine when after shutting the car down (but not the radio off) it would turn off the radio in less than 5 minutes (as opposed to 20). Basically, a symptom led to the icon. Why doesn't it do that for the OP's situations (especially #3)?

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'08 X5 3.0si - Alpine White / Saddle Brown interior
Specs: Sport Pkg, Premium Pkg, Tech Pkg, Comfort Access, Aero Kit, Style 433 staggered 20s on Conti DWS
Mods: Carbon 35 tint, LED angel eyes, GP Thunder 7500k fogs, H&R 20mm/25mm spacers, clear reflectors, gunsmoke-tinted taillights
Coded: Digital speedo, windows/sunroof/tailgate close via keyfob

X5 pics at Flickr