On another note my wife just bought a new computer and is having the same problem and window saying the same exact thing but while she is trying to download World of Warcraft onto the new computer. We then tried installing WoW with our discs that we have. It did instal fine we think. But as it got to mists of pandaria updates it froze and says the same thing again. (Failed to download a required file. Please check your internet connection and try again.)
I'm assuming that there is a problem with Blizzards downloading and or updating site.