Okay, that at least is displaying a form, but it's been edited and customised. I'm not sure if that's what also broke it.
Also, I cannot find a WordPress page on your site that handles subscriptions and unsubscriptions as recommended in the Installation instructions.
So, first thing to do is create that page and direct your widget to that, also set the page as the core plugin page. If that doesn't help you need to revert to the original code of the plugin and see if that restores the functionality. (For example the existence of 'submit' $_POST input is important in the plugin yet on your form you've switched to an image button.