Thread temporarily suspended. Thanks to all here!
YoKenny general advice are nice, but I don't have much time to edit a host file, and it's out topic anyway.
It was a serious matter to rule out a similar case on someone else's machine. Disk4mat did answer my question, as others after him The first step to troubleshoot my system was then to remove CCleaner and to re-install it. It seems to work fine now.
In the first installation, the cookies were removed from the system, only the list was remaining in the CCleaner window, hence, the browser was probably not the direct cause.
Nevertheless, I will try again in a couple of days and get back to the thread.