I just tested with IE10 Release Preview on Windows 7 using your site. The Like button works fine for me, but clicking the Login with Facebook button correctly shows the login popup, but doesn't redirect. Is that what you see?
The issue is likely due to a Javascript error on your page. If you hit 'F12', and go to Console, when the page loads (before you do anything with Logging in), there's a jQuery.js error on line 2 at character 68522. I don't know what that error is, and JFBConnect doesn't even use jQuery, so it's not from us. However, when you have a Javascript error, that can prevent any other Javascript functions from running. JFBConnect needs our jfbconnect.js file to run, and it simply looks like it's not executing. You'll need to narrow down what the jQuery error is and get rid of it, then things should work.
I tested IE10 on this site, and a few others, and things work just fine with the Login functionality, so it seems more specific to your site.
Let us know how that goes, and good luck,
Alex