First I tried to to just clear the cache in Recovery Mode. It went into a long loop where every other second a flash would appear on screen with the 'No Command' screen. I decided to abort that after 30 minutes and try a Wipe data/factory reset in recovery mode.
It seems to work fine in the beginning, but after a while it begins with the same loop, where it occasionally shows the 'No Command' screen.
Seems like there is broken hardware - or do you have any ideas what the reason may be and how to amend it?