Form submission not working in template file
You can render form specific form elements with the help of drupal_render. And in order to make submit button work, render all hidden form items and your submit button will work fine then.

Necessary fields for form submission are:

echo drupal_render($form['form_build_id']);
echo drupal_render($form['form_token']);
echo drupal_render($form['form_id']);


and ofcourse your submit button too.