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Button is overriding/conflicting with another button on the same webpage
<input id="show_hint" class="button" type="submit" value="Hint" onClick="location.href='#hint'" />

// Button 1
$(function(){
  var count = 3,
      $btn = $('input[type="submit"]');
      $btn.val($btn.val()+' ('+count+')')

  $btn.click(function(){
      $btn.val($btn.val().replace(count,count-1));
      count--;
      $('#hintscore')
        .hide()
        .css({
            bottom: 30,
            left: 300,
            opacity: 1,
        })
        .show()
        .stop()
        .delay(200)
        .animate({'bottom':75, opacity: 0},1000);

      if(count==0) {
            return !$btn.attr('disabled','disabled');
      }
  })
});

<input id="showmenu_win2" class="button" type="submit" value="Menu" />

$('#form').submit(function() {
        $.ajax({
            type: "POST",
            data: $("#form").serialize(),
            cache: false,
            url: "insert.php"
        });
        return false;
    });

$btn = $('input[type="submit"]');

$btn = $("#show_hint");

$btn = $('input[type="submit"]');

$btn = $('#show_hint');

$btn = $('#ancestor-element').find('input[type="submit"]');

$btn = $('input[type="submit"]').not($('#form').find('input[type="submit"]'));

<input id="show_hint" class="button" type="button" value="Hint" onClick="location.href='#hint'" />

$(function(){
  var count = 3,
  $("#show_hint").val($(this).val()+' ('+count+')')

 $("#show_hint").click(function(){
  $("#show_hint").val($(this).val().replace(count,count-1));
  count--

 // Your remaining code...

<input id="showmenu_win2" class="button" type="input" value="Menu" />

$('#showmenu_win2').click(function() {
    $.ajax({
        type: "POST",
        data: $("#form").serialize(),
        cache: false,
        url: "insert.php"
    });
    return false;
});