I think the situation with my Garmin (10R-04 6953 4NSF, branded for Volkswagen) is exactly the same as grodan's. It runs the vw animation and freezes black.

I have disconnected the battery which was already dead (0V at the battery connector, on the other side of the battery protection circuit there was something like 2.6V). I replaced it with a charged 18650 cell (kept the 3rd wire and GND still connected to the original battery) but it will not turn on with the power button. It does turn on if I connect it to PC first and then push power.

I tried the factory reset but it goes black shortly after touchscreen calibration.

Navigon Fresh recognizes "My System" (NAVIGON VW_PID_V2 version 7.16.8) and can even back it up!!!

Links in [Only registered and activated users can see links. ] seem to have died. Also I have 7.16.8 so probably things would not improve if I managed to "update" to 7.10.25...

Many of the Garmin links have died too but I don't even know what to look for - there is no "10R-" anything or "4NSF" anything or "NVO" anything.