How you are embeding the you tube video.?
If you are using HTML5 Video tag then, use the end event handler.
<input type="button" id="myButton" value="Submit" /><br />
<video id="myVideo" controls src='<%= ResolveUrl("~/Files/1658.mp4") %>' width="200" height="250" />
<script type="text/javascript">
window.onload = function () {
var video = document.getElementById("myVideo");
var button = document.getElementById("myButton");
button.disabled = true;
video.addEventListener("ended", function () {
button.disabled = false;
}, true);
};
</script>
Screenshot