There's users using FireFox and chrome and successfully playing the game. This is without doing anything but logging in.
Until we know exact details on what can be causing this it's hard to explain to users what they might be doing wrong or what is at cause. Right now this is still being worked on and we cannot find any issues caused since many players have it working already.
Try another computer for the sake of just trying, install different browsers, make sure you are connected directly to the internet without any proxies or other internet settings, do not have private browsing enabled, make sure your browser save cookies from the sites it visits, make sure you enter your username correctly with all Capitalization the right etc etc.