If you open a command prompt and type "ping content.warframe.com", does it resolve to a server name (probably something ending in akamai.net) and give a ping reply?
If it does not, then you have a problem with your DNS settings or your ISP, not the game's fault.
If you can successfully ping Warframe's content servers, click the "Get Logs" button in the launcher's Config menu (the little gear icon) and send it to Support. Or look in the file "Launcher.log" if you're tech savvy. It might have some hints as to what is going on.