No, that's not something we can do. Using another user's Facebook credentials are something we shy away from as it's a violation of Facebook Policy and that's something we want to be on the right side of to prevent any repercussions.
I'm unsure why it's not working, but again, if you disable the JFBCSystem plugin (and clear caches on your site) and things still don't work, it means something else is going wrong. That could be another extension conflicting, an App mis-configuration issue or something else that I can't think of.
While we'll always help with any JFBConnect-specific areas, general Facebook administration is something that we don't do regularly either and I'm not sure we'd have much more experience or better results doing so.
Of course, if you have any questions, we'll gladly try to help as best we can, Page administration just isn't our expertise.
Alex