Okay I finally found an easy and kinda great solution 😉
The problem is indeed about connectivity. It seems that during the Activating and Time setting process, the ATV has to connect to Apple or iTunes servers through a special port or connection.
My device was definetely connected to the internet, because I could check and download new updates and all my other devices on the home network were connected to the internet but still it wouldn't get activated.
So, today my Apple TV 3rd generation arrived and after setting everything up I also faced the "Setting Time and Date"-problem.
First, the ATV was connected to my router via WiFi.
Like everyone else's case the ATV would stuck on the "Activating - Setting Time and Location"-Screen.
When I would skip the Activating screen there were only 2 buttons on the ATV Home Screen, "Computer" and "Settings".
I did everything everyone suggested here, but it didn't work for me.
Then I connected it via Ethernet, but still, same thing.
I also let it go for a couple of hours, but still no luck.
Then I did a really simple thing:
I used the Personal Hotspot on my iPhone so the ATV would connect to the internet via my phone carrier.
And bamm, after only seconds it worked!! 😉
After everything was loaded and I logged in with my Apple ID and turned Home Sharing on, I connected the ATV back to the router.
Now everything works fine!
As I described, there might be conflicts between the ATV, trying to use special ports, and your home internet connection.
Since there are nearly no restrictions when you use your phone's data I thought that maybe that might be a solution which indeed was right!
Hope this works for everybody and enjoy your ATV! ;