I had the same issue.
The lighting on the logo does not comes from a LED but from some kind of electroluminescent material on a thin plastic PCB.
The adapter, (the cube) is a plastic box filled with some kind of resin and containing an electronic circuit.
I saw that my adapter was not outputting anything.
I tried to broke the plastic and resin without damaging the electronics. finally I was able to access to the PCB but not the electronics compound.
I replaced input and output wires.
It appears that the adapter , with a 14VDC input, have a 7VAC output with nothing plugged in.
If I plug the electroluminescent logo, it outputs... 90VAC !!!
The logo works back, the light is very low and but is only visible in the dark (but it was ever the case previously).
EDIT: photos added.