There's 1 definite issue and another possible problem.
1) Your PHP installation has cURL installed, but it's explicitly disabled. cURL is required by Facebook for authenticating users and multiple other features. It's also used by JFBConnect for our Autotune program to configure your site automatically.
If you go to Site -> System Information and then the PHP Information tab, you'll find the following line:
disable_functions exec, passthru, shell_exec, system, proc_open, popen, curl_exec, curl_multi_exec, show_source
That line is disabling multiple functions which generally should be disabled. However, curl_exec can't be one of them. Usually, that line is a setting in your PHP.ini file, but depending on your hosting company or if you're using cPanel/Plesk, you may find the setting elsewhere. You'll need to remove curl_exec from the disabled list and restart Apache.
2) The securelive_system plugin was making it hard to diagnose anything because it kept thinking I was a bad guy. If you run into issues after re-enabling cURL, you may want to try disabling this plugin (temporarily) to see if it helps.
I've noted a bug in our to-do list to not just check if cURL is installed (what we do now) and explicitly check that it's usable. Right now, it's incorrectly reporting that it's enabled on the Autotune home page for you. Sorry about that.
Please let us know if you need any more information or help, and sorry again for the delay!
Alex