Persistent "No connection"

When the launcher is opened, and I'm certain to have an Internet connection, Minecraft Launcher says I'm not connected to WiFi, displaying "No connection" in the top left corner that won't go away no matter how many times I hit the refresh button, and makes me play only in offline mode. Also, can't connect to any server either: the game just fails to connect displaying "Timed out"

I've bought the game today and this is driving me crazy. PLEASE FIX THIS.