Usually, when the Login with Facebook button doesn't show up, it's because the Facebook Javascript library couldn't be loaded on your page. This is usually due to using a language on your Joomla site that Facebook doesn't support or from a Javascript error on your page that's preventing the Facebook library from loading.
If you could, go to the configuration area of JFBConnect, click on the Facebook API tab, and try putting en_US in the language setting box. If that works, use the link next to it to load a list of languages that Facebook does support.
Hope this helps, but if not, post a link to your page, and we can diagnose things a lot better.
Thanks,
Alex