Another add-on to that:
* Don't minimize or close the tab, you must keep it open. You can minimize it once you get logged into the game, though.
* Use a browser that will work for you if you still continue getting problems.
* Type your username and password in correctly and carefully on both, the login page and ingame login. Just in case!
Adding on to what the other helpful floofs above said, make sure your username is LESS than 16 characters long, otherwise the game will not let you log in. And the only way to fix this is to make a new account at the next open registration.