Just to say that I am having the exact same problem.
I got the beta today, tried it for about an hour and it all worked fine. However, after loging out and trying to log back in a while back, I hit this 'Unity not loading' wall.
I tried clearing cookies from the browser but that didn't change anything. I am using a Macbook Pro with OS X 10.6.8, Firefox 11 and Chrome 17.0.963.79.
Hope this helps track down the problem...