Talos263: First off... Thanks to everybody. I will test everyting and tell if something works ;)
If the game runs in the background (look in the task-manager) after you clicked the play button you could try this:
Q.: When I start the game nothing happens, but I can see the application running in the background.
A.: There has been a solution circling around that worked for quite a few people, thanks to Hycinthus:
1. Uninstall Galaxy
2. Open command line (Start->type "cmd" -> right click "cmd.exe" and click "run as administrator")
3. Type sc delete GalaxyClientService
sc delete GalaxyCommunication
4. Go to //gamedir\bin\x64 and rename or delete galaxy.dll
5. Launch the game, an error message will pop up, but the next time you start it everything should be fine
Source:
http://www.gog.com/forum/the_witcher_3_wild_hunt/faq Don't forget to backup the save files and game install files first!
Good luck!