The cause: many dead electrolytic capacitors + blown DC-DC regulator.
The MD5001T is used to generate 1.8V (core voltage?).
It was reasonably easy to fix: desolder bad caps and replace, desolder SOIC-8 IC and replace. Done. The only caveat: the PCB is a single-sided phenolic one, so no plated holes! The traces lift extreme easily, watch out!
The device is very modular, which is good. Nevertheless I had to remove every single PCB, the DVD drive and the hard-disk to get access to the underside of the large circuit board.
A few things surprised me:
Apparently it is still cheaper to have a single-sided phenolic board and be forced to use a “wire-jumper-machine” than to just order an ordinary 2-sided circuit board.
The large black connector that goes to the “brain” (HDD-controller, DVD-controller…) is unpolarized! Once the device is more or less assembled, there is no way to connect it wrong (no space), but during debugging… one could plug it in the other way.