Captcha won't show up when load contact form by Static Block

I think that you have the js issue,

in app/design/frontend/{package}/{theme}/template/contacts/form.phtml

replace

<script type="text/javascript">
//<![CDATA[
    var contactForm = new VarienForm('contactForm', true);
//]]>
</script>

With:

<script type="text/javascript">
//<![CDATA[
    var contactForm = new VarienForm('contactForm', true);
    function validateCaptcha() {
        var v = grecaptcha.getResponse();
          if(v.length == 0) {
               jQuery('#error-g-captcha').show();
               return false;
          }else {
              jQuery('#error-g-captcha').hide();
              return true;
          }
    }
//]]>
</script>