SCLogin is not required to be published for the Like buttons (or any reason, really). It's just an easy way to add the Login with Facebook button, if you want to use it.
The problem seems to be a wonky redirect on your page and some security measures from Facebook. First, of Facebook wants to 'see' the content of your pages that people can Like. While some being hidden behind a paywall is fine, Facebook wants to see at least a few pages to understand what type of site you are. Currently, there are no Like buttons on pages that Facebook can see.
Now, for the why part of why can't Facebook see the pages. If you go to the following page:
http://www.myjohnstownbreeze.com/index.php?option=com_content&view=article&id=7450:riders-reds-go-to-overtime-in-roosevelts-regular-season-opener&catid=1:latest-news&Itemid=50
There's a Like button on that page that is 'for' that page. Since that page is public (at least part of the content), Facebook should be able to see it. However, JFBConnect is inserting an Open Graph canonical url property that says the page is really:
http://www.myjohnstownbreeze.com/index.php?option=com_content&view=article&id=7450:riders-reds-go-to-overtime-in-roosevelts-regular-season-opener&catid=1:latest-news&Itemid=50
Those URLs are almost identical, but the difference is that the first URL uses & instead of &. Either should work (and Facebook prefers the simpler & symbol). However, if you go to the 2nd URL, it redirects to the CB Subs page. That doesn't seem right to me, and the fact that it doesn't work is going to be bad for Facebook and even search engine purposes.
To see the effect it has, check out the following URL Debug Tool from Facebook:
developers.facebook.com/tools/debug/og/o...%26amp%3BItemid%3D50
You can see the redirect chain it's going through and the ultimate page (without any Like button) that's being arrived at. Not sure where the problem lies, but hopefully this long explanation will help you narrow things down!
Best of luck, and let us know if you need more help,
Alex