- Clear cache and cookies, and restart your browser.
- Login using the new, improved Blogger Login screen.
You'll have separate, well defined choices.
- Old Blogger, using your Blogger account.
- New Blogger, using your Google account.
But the first time that you use the new login procedures, be sure to clear cache and cookies, first. Blogger appears to be reusing addresses, cookies, and scripts, even though they are providing a new set of servers ("www2.blogger.com", instead of "beta.blogger.com", for instance). If one of your cookies continues to point your browser to "beta.blogger.com", guess what will happen?
No, I can't say for sure. But I'll bet that you're not as likely to see your dashboard, when it does.
Start cleanly, and clear cache and cookies, before you login to The New Blogger for the first time.