Yeah it seems that I have magical forces.
I...
-recharged the battery cells with my microcontrolled quick charger
-cleaned the upper and the bottom side of the cells with "Liqui Moly Multi Spray Plus 7"
-pulled out the battery springs a little bit
-cleaned them with Liqui Moly too
-cleaned the 44 pins of the hard disk, also with that Liqui Moly spray
then I re-assembled the device. And now everything works fine and I'm listening to my root.m3u.
8-)
-Bumping the device carefully on the desktop doesn't affect anything - nice!
-next test is: playing until the batteries are empty and trying to recharge them in the player...
But what shall I do with that nice Fujitsu 120 GB drive now? If I send it back and the Jukebox works fine during the next years I would probably often be annoyed because of that 20 GB limit (somehow I filled the Hitachi with 19 GB during the last three years...).
When I decide to keep it and upgrade my AJR with it - what if the device finally dies in november? I think since it is a 4200 rpm drive it only makes sense to be used in a device like a Jukebox. For use in an external HDD case  or in a laptop I would rather take 5400 rpm drives...
What if I decide to upgrade my AJR, and after partitioning and formating the fujitsu and replacing the old HDD the AJR doesn't start up anymore?