tag. Only the fields within these tags are considered part of the form. The tag, that is your "submit" button, is out side your form. It must exist before the ending tag or it will do nothing.
Either move the tag, that is your "submit" button, inside the form, or go back to the E-Mail Form service manager and copy/paste the form again. The code in the E-Mail Form service manage has the "submit" button in the proper place.
