Similar thing here.
Typed my info into the launcher, clicked login, patcher seemed to work his thing a bit slow but after a while the magic play button appeared. I launch the game and the server list is empty. No servers listed.
So I restart the game...
Can't get past the launcher now. Just gets stuck after putting in my credentials.
EDIT: Played yesterday just fine with everything the same. Nothing has changed on my PC or with my internet provider. So my WILD GUESS is something is wrong on your side... again