My first and obvious guess is that the JFBConnect install you're using is too old. However, sometimes we do conflict with other extensions that integrate with Facebook. JFBConnect uses the recommended javascript library from FB, but there are still some extensions that have not been upgraded to the current library - which causes login/social widget/etc functionality to break. Without seeing what you've added, I wouldn't know which it is. Could you point me to a URL that has the chat or provide the code that you added?
That being said, version 7.0.2 from 2 years ago is definitely outdated. Facebook has changed extensively in that time period. I'd be surprised if all of the functionality is still working in that JFBC version...
-Melissa