Javascript form validation not working with channel from

<form id="formElem" name="formElem" action="" method="post">

{exp:channel:form include_jquery="no" class="new_customer" id="formElem" error_handling="inline" name="formElem" channel="pets" logged_out_member_id="1" status="Pending" return="pet/review_submit_thanks"}

<form>

$(function() {
 /*
 number of fieldsets
 */
 var fieldsetCount = $('#formElem').children().length;
 
 /*
 current position of fieldset / navigation link
 */
 var current  = 1;
    
 /*
 sum and save the widths of each one of the fieldsets
 set the final sum as the total width of the steps element
 */
 var stepsWidth = 0;
    var widths   = new Array();
 $('#steps .step').each(function(i){
        var $step   = $(this);
  widths[i]    = stepsWidth;
        stepsWidth   += $step.width();
    });
 $('#steps').width(stepsWidth);
 
 /*
 to avoid problems in IE, focus the first input of the form
 */
 $('#formElem').children(':first').find(':input:first').focus(); 
 
 /*
 show the navigation bar
 */
 $('#navigation').show();
 
 /*
 when clicking on a navigation link 
 the form slides to the corresponding fieldset
 */
    $('#navigation a').bind('click',function(e){
  var $this = $(this);
  var prev = current;
  $this.closest('ul').find('li').removeClass('selected');
        $this.parent().addClass('selected');
  /*
  we store the position of the link
  in the current variable 
  */
  current = $this.parent().index() + 1;
  /*
  animate / slide to the next or to the corresponding
  fieldset. The order of the links in the navigation
  is the order of the fieldsets.
  Also, after sliding, we trigger the focus on the first 
  input element of the new fieldset
  If we clicked on the last link (confirmation), then we validate
  all the fieldsets, otherwise we validate the previous one
  before the form slided
  */
        $('#steps').stop().animate({
            marginLeft: '-' + widths[current-1] + 'px'
        },500,function(){
   if(current == fieldsetCount)
    validateSteps();
   else
    validateStep(prev);
   /* $('#formElem').children(':nth-child('+ parseInt(current) +')').find(':input:first').focus();*/
   $('#formElem').children(':nth-child('+ parseInt(current) +')').find('.required').focus(); 
  });
        e.preventDefault();
    });
 
 /*
 clicking on the tab (on the last input of each fieldset), makes the form
 slide to the next step
 */
 $('#formElem > fieldset').each(function(){
  var $fieldset = $(this);
  $fieldset.children(':last').find(':input').keydown(function(e){
   if (e.which == 9){
    $('#navigation li:nth-child(' + (parseInt(current)+1) + ') a').click();
    /* force the blur for validation */
    $(this).blur();
    e.preventDefault();
   }
  });
 });
 
 /*
 validates errors on all the fieldsets
 records if the Form has errors in $('#formElem').data()
 */
 function validateSteps(){
  var FormErrors = false;
  for(var i = 1; i < fieldsetCount; ++i){
   var error = validateStep(i);
   if(error == -1)
    FormErrors = true;
  }
  $('#formElem').data('errors',FormErrors); 
 }
 
 /*
 validates one fieldset
 and returns -1 if errors found, or 1 if not
 */
 function validateStep(step){
  if(step == fieldsetCount) return;
  
  var error = 1;
  var hasError = false;
  /* $('#formElem').children(':nth-child('+ parseInt(step) +')').find(':input:not(button)').each(function(){ */
  /* $('#formElem').children(':nth-child('+ parseInt(step) +')').find('.required').each(function(){ */
  $('#formElem').children(':nth-child('+ parseInt(step) +')').find(':input.required:not(button)').each(function(){
   var $this   = $(this);
   var valueLength = jQuery.trim($this.val()).length;
   
   if(valueLength == ''){
    hasError = true;
    $this.css('background-color','#FFEDEF');
   }
   else
    $this.css('background-color','#FFFFFF'); 
  });
  var $link = $('#navigation li:nth-child(' + parseInt(step) + ') a');
  $link.parent().find('.error,.checked').remove();
  
  var valclass = 'checked';
  if(hasError){
   error = -1;
   valclass = 'error';
  }
  $('<span class="&#039;+valclass+&#039;"></span>').insertAfter($link);
  
  return error;
 }
 
 /*
 if there are errors don't allow the user to submit
 */
 $('#registerButton').bind('click',function(){
  if($('#formElem').data('errors')){
   alert('Please correct the errors in the Form');
   return false;
  } 
 });
});