I can count about 9 DAB radios in my house - they all have external AC/DC power adapters.
I guess that they do this to prevent an internal mains transformer causing interference if placed inside the enclosure.
My experience tells me that a common failure mode with AC adapters is a broken conductor - unseen and inside the insulation - invariably where the wire bends at one end or the other.
I also guess that what you seek is very probably not available.
Amazon sell replacement adapters for your radio 7.5V
Good Luck...
May 2016