How to deal with a domain thats in an inconsistent state?

I have a domain that's just being used for emails and the user cannot log into the control panel to do anything.. how do I backup up their emails and redo the users' profile? Ive noticed that the CWP panel doesnt backup emails, or I could be wrong..

Help?

I have this exact same configuration, with a domain just used for emails, and I can work normally with it.
But the domain is configured normally, and is not in "inconsistent" state, it is enabled normally, but I only disable the "www" at DNS configuration.
This is the only change I made.
The control panel is accessed normally too, in the customer panel.

With backups, I do it manually with a custom remote backup script.

Regards,
Netino