The lithium battery is dead. It looks like it’s soldered or glued in place?
Soldered probably. I’ve replaced one in a BC9500 but not a BS4000. You need to be a little careful soldering lithium batteries – not too much heat! Alternatively some people have replaced the battery with a small lithium battery holder to make it easier to replace, but if there is limited space you may need to relocate this within the Beosound.
Not sure if this is the right one for a BS4000 (check the manual) but this is the one I got for my BC9500: https://uk.farnell.com/renata/cr2450-nfh-lf/cell-lithium-button-2pin-3v/dp/1319731?CMP=i-ddd7-00001003
