Here is html code for the form:
You need to include the validation script in the head of your document.
Like this:
Also, please check in the rendered HTML that your form ID is correct.
I use this code for calling validate on my sites
//Validate Form
var ids = [];
$("form").each(function () {
ids.push(this.id);
});
var formId = "#" + ids[0]
$(formId).validate();