(And I know the Google team is listening to this right, because they can listen to everything?)
It turns out that if you are being invited to the new blogger beta and you have not made your own blog first or switched (which you cannot since slots are limited) you will be in a state where you have access to a blog but have not signed the terms of service! The result is that the edit bar
will appear but any attempt to do anything will put you in a login dialog box that will simply repeat forever, giving no indication of why the login failed to work.
The solution is to start to create a new blog, just to accept the terms of service. Then abort that process and go back to the blog you were invited to and it will work. Obvious!!