I have the old email version still in use for one email account, and the email folders column at left is still there but completely blank. It's not that it isn't expanded or anything like that; the column is there but it is just white space. Also, I tried selecting an email and clicking the move button to see if I could gain access to a folder in that way, but nothing happens when I click that button. On another account I have the new email set up and it is fine. I would change the old one to the new one but I can't find a way to do that. Any help?
Try clearing out your browser's cache/browsing history. When you have done that, close out the browser and re-start it in a fresh session. If that doesn't do it, then try using a different browser.
And no, there is no way for you to get into the new format yourself. You just wait for it to happen. As of a couple of weeks ago, the migration was about 98% complete. So it shouldn't be too much longer for you.