I have a form with multiple inputs, select boxes, and a textarea. I would like to have the submit button be disabled until all of the fields that I designate as required are
I recommend taking a slightly different approach and using jquery's validation http://docs.jquery.com/Plugins/validation. The tactic you are suggesting is prone to security holes. The user could easily using firebug enable that button and then submit the form.
Using jquery validation is clean and it allows you to show error messages under the required fields if so desired on submit.