Uncaught TypeError Object [object Object] has no method 'datepicker'

I am getting this error when my page loads:

Uncaught TypeError: Object [object Object] has no method 'datepicker'
(anonymous function)
(anonymous function)
b.extend.globalEval
b.fn.extend.domManip
b.fn.extend.append
(anonymous function)
b.extend.access
b.fn.extend.html
(anonymous function)
c
p.fireWith
k
r

Screenshot

I thought it may have to do with a Jquery conflict, so I add $.noConflict(); before the function call. Still I am not sure how can we see if there is Jquery conflict present in our page or not.

Here is my code:

<script src="../js/jquery-1.9.1.min.js"></script>
<script src="../js/jquery-ui-1.10.2.custom.min.js"></script>

<!-- 
  <script src="http://code.jquery.com/ui/1.10.3/jquery-ui.js"></script> 
-->

<link type="text/css" href="jquery.datepick.css" rel="stylesheet">
<script type="text/javascript" src="jquery.datepick.js"></script>

<?php
  echo "<script>User();</script>";
?>

<link rel="stylesheet" 
  href="http://code.jquery.com/ui/1.10.3/themes/smoothness/jquery-ui.css" />

<script>

  $(function() {
    $( "#fast" ).datepicker();
  });

</script>

<script>
  $(function() {
    $('#modal').draggable({ handle: "p" });
  });
</script>

My major question is how we can see if conflicts exist or not and how to remove them. What does this error mean and how can I fix it?