We've been spending quite a bit of time trying to figure out what is causing the recent spate of issues with LIVE (hanging on the login screen). We believe it has something to do with a recent update to Java, but we are not sure.
One thing we know is that if you experience this, you can close your browser and try it again and it may work. You may have to do this a couple times.
For us, it worked. Next time, it worked. Next time it hung. Next time it worked. Very strange.
That's at least a short-term fix until we can find the root cause.
Thanks for your patience and sorry for the delayed response to this issue.