According to your instructions:
4. Enter your MailChimp API Key and let the plugin verify it.
In MailChimp Setup, there is nowhere to enter my API. It take me directly to "connect" and I can't connect unless I connect externally (by going to mailchimp.com first) - THEN it let's me connect via WP. Then I can see my list and I have a MC widget, but as soon as I log out of the MC site, my widget goes away - ??? I'm thinking this has something to do with not being able to find an input for the API.