I have the same or at least a similar probleme.

It started relatviely normal with GMXMail Check telling me to delete the Cache and I could still see my e-mails when I used this extension.

Deleting the Cache didn't help at all. I (also) deleted and reinstalled the extension - now I can't use GMX at all.

When I want to use the extension to log in I can't even write the password.
When I try to log in normally I can write the password BUT I can't get to my mails. GMX doesn't stop loading.