Can't log in - authenticator dead

I'm trying to get back into my account, which I haven't accessed in several years. I had a physical, electronic authenticator key for two-factor authorization, but the key is now dead and doesn't respond at all. Is there a way to log in to my account without it? I would prefer not to lose all of my characters, items, etc. (Alternatively, if there's a way to contact support that doesn't involve calling the number, that would be great.)