It sounds like it might be a connection issue. If it works fine on broadband, and assuming you are using the same computer of course, then the only difference would be your wifi. I have to ponder the question of if your wifi is somehow limiting your bandwidth to the point that it isn't allowing you to load the game.
I sometimes encounter a similar problem if I have too many devices connected to my wifi, and one or more of those devices is down loading something. If you don't mind, try seeing if you have other devices on your wifi that could be drawing on the connection to the point that it doesn't work.
Like I said if the only difference is the wifi, then it stands to reason that it is your problem. Good luck sir. Also please post here if you have any additional information.