"An unexpected error has occurred while trying to install. Please try again or contact Customer Support."
So I tried everything:
I deleted the files that were downloaded by the Blizzard Launcher and re-downloaded them again.
I also restarted my computer, and tried again.
I also tried to run the installation as administrator (Right click ---> Run as administrator).
All has failed.
So I then tried to download the US English version of the installer.
Weird - for some reason it is 31 MB (Diablo-III-Setup-enUS.exe), while the European version is 7 MB (Diablo-III-Setup-enGB.exe), hmmmmm...
Anyhow, the US version doesn't download new files for some reason, and goes straight to installation. I think it somehow finds the files I used with the European version (???).
I might have created some weird conflict... idunno..
Anyhow, the US English installation also fails with:
"Failed to download a required file. Please check you internet connection and try again."
I don't have any internet problems. This simply can't be the problem.