A little update:
Today I first tried to update 4 other WP-sites (my own sites) –> no problem.
The site that this topic is about is for a customer, so I’m more careful with it. I don’t see the difference really between these 5 sites (only the theme).
Tomorrow I will try again to update this one.
By the way: I’m not sure if this applies: <i>”Not sure if you’ve tried this already, but can you deactivate all your plugins and switch to one of the default themes (twenty thirteen/ fourteen etc.) to narrow down the issue?”</i>
I have downgraded to 3.8.3 first, so the site was online.
When I updated to 3.9 nothing was psooible, I couldn’t login to the backend. If anything was possible it was by FTP.
Anyway: I try again tomorrow.