I had this problem ever since my Windows 8 updated to 8.1 (not everyone has this problem)… I could only connect with Firefox. Of course java is up to date and I did it many times with same results. Strangely, if I create a new user account on my Windows, IE 11 works fine.
Finally I solved it and the solution was very simple.
When you go to wdmycloud.com, you enter your email address and password and you click “submit” nothing happens. Stay on the page, in the url address bar at the top, you will notice a stop/block sign (a circle with a line across it in blue). This indicates that the site is blocked. Click on that sign and unblock it. That is it, everything is working now.
My current java version is 1.7.0_55.
Hope this helps someone.