Some news about my Onkyo 616. It's still not working, the old problem still exists. So I decided to get another one, but as I read that the 414, 515 and 616 series (new models) all seem to have serious problems with HDMI, there's even a thread in the AVS forum only about that, I decided to get the bigger model, the 717, which apparently is not affected by that problem.
He will take the old one back, he told me that Onkyo would take it back, and it will be possible to make a change. Will only have to see how much I will have to pay, as the 717 is almost double the price, like almost 1.000€.
Only problem at the moment is, that Onkyo wants the complete receiver returned, including accessories, which is not the problem, but they want it in the original box, which I don't have anymore, and my reseller also doesn't have a spare 616 box left. But he told me that he's gonna manage it somehow.