You are correct that you'll need the action attribute to process the form. You'll also need the method attribute eg
I haven't looked at the attached files, but if there's CSS attached to this form, then you're going to need to re-add
class="button1" to the submit button. Also, as it is now a button you'll need to add a couple of extra lines to get rid of the default button style.
Note you also missed the
value attribute from the submit button.