Disabling WP Social Login Plugin Breaks Theme

Hey there. I had a custom theme created by a Freelancer, and he installed WP Social Login Plugin which allows you to log in using various social networks. I have had non stop problems with the plugin, with the most annoying being that once you log in, the site still thinks you are logged out and you can't access any member features. After much troubleshooting I have decided to remove the plugin and go for an alternative (Probably Ultimate Facebook for now), however when I attempt to remove the plugin, it completely breaks my theme and only loads a white visual bar at the top.

The code is implemented in a small login window on the website as that is where the buttons are to be able to log in with Twitter, facebook or Google plus. I assume that removing that code will allow me to remove the plugin without causing issues.

The buttons are also visible on the following page: http://searchbuzz.co/register

If anyone has any ideas on how to get this plugin removed, that would be great. To avoid any confusion, it is the following plugin: