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No solution, compatibility issue with wireless router (Orange, Livebox 3) and Chromecast. Returned chromecast to point of sale.
After a week and a dozen hours of trouble shooting, I've come to the conclusion that it is a compatibility issue between the chromecast and my carrier supplied wireless router. I am with Orange in France, and I've seen on other forums that people with the same setup are having problems with chromecast. Some had success with changing some settings (see steps marked with *) but I was not so lucky.
What I tried: