That is unsupported addon which has option {$xenOptions.c2Twitter_consumerKey} mentioned by
This (my) is supported and I already told you that the reason of it's not working for you is custom style.
If I had access to style I could say what exactly matters. It may be a hook missing, var $eAuth=false or whatever.
If the style loads native untouched template "login" instead of "login_bar" than it of course not gonna work since this template has no hooks at all.
Any button can be easily added by editing template or creating modification in TMS.