Somehow your game is "stuck" and you can't connect to it. What you need to do is the following:
1) Open "dominion.games" in an incognito (Chrome) or private (Firefox) window.
2) Enter your name and password, but do not click "Login"!
3) Instead, click the "Kick" or "Kick & Resign" buttons (in small print at the bottom of the side).
After that is done, you can close the incognito/private window and log into dominion.games as normal.