Glad that got your Facebook button going.
For LinkedIn, the problem isn't directly related to JLinked. The issue is that there's some sort of Javascript error on your page that is preventing our Javascript from properly initializing, and will likely cause you other issues. When the page loads, in the Javascript console, is the following error:
Uncaught SyntaxError: Unexpected token ILLEGAL www.atjump.com/:102
That line is coming because you added additional permissions requests to the JLinked configuration area, but are adding them on new-lines, not as comma-separated values. That's breaking the Javascript and causing the error. In general, you shouldn't need to define the permission values unless you're doing some custom coding. Our profile plugins will automatically request the needed permissions.
Directly after that error is where our jlinked variables are defined. Specifically, the jlinked.base varable, which should just be your home page. On your site though, because of that error, it's undefined, which is why the redirection is going to your site with undefined in the link.
Remove those permissions, or put them in correctly, and things should start going.
I hope that helps,
Alex