I am having the same problem. I used the mock draft yesterday with no problem. I even had a live draft with no issue. I followed your advise and updated Java not once but twice just to make sure. Still doesn't work. Thanks for looking into this. My browser is IE9.
Try uninstalling previous versions of java from the control panel and then install the newest one again from java.com.
Your best bet for now might be to download a new browser (try google chrome).
If you need further help troubleshooting, please email us at fleaflicker.com and we can help you in a much more detailed fashion.