I asked the Sony support about the internal battery assuming this is the one for to remember the settings and they said 3 month. Looking back at my Nex6 in the shelf it wont run out of internal battery within a day. Popping in the battery after a couple of month and it restarted with all the settings. No need to change the time.
Anyhow, no matter if the battery runs out in a day or after 3 month, since I cant exchange the internal battery to have a reset and hope for a resurrection - my camera is dead.
Offtopic: I also asked for the star eater problem and they confirmed working on a new firmware that solves the problem.