I've made some progress.
Got a TTL to USB adapter, connected GND, RX, Tx to Kindle serial pads.
Got to u-boot.
Booted kernel.
Logged in as framework:mario got shadow
Cracked root with password fiona***:
http://openinkpot.org/wiki/Device/Kindle3/RootShell
Still there are various problems constantly: serial connection is rather unreliable, possibly fault of the adapter but who knows.
Also, the micro USB cable is giving problems and I had to dowshift to USB 1.1 to be able to copy larger files.
It appears, the battery was run down completely and now it has problems charging and it discharges quite quickly.
Next step is going to be dissasemble the DX completely and see if I can get any signs of life into display.
I still refuse to believe that a display can fail completely. Hope dies last .
Forgot to add, to start the whole thing I had to hold down power for 15 seconds or so as usual.