これでうまくいくはずですが、'video' と 'image' がそれぞれの URL を指していることを確認してください。
<script>
function doVideo()
{
var video = "myvideo.mp4";
document.getElementById("videoimgdiv").innerHTML = "<video autoplay onended=\"doImage()\"><source src=\"" + video + "\"\></video>";
}
function doImage()
{
var image = "http://us.123rf.com/400wm/400/400/podlesnova/podlesnova0906/podlesnova090600034/5117393-small-red-furry-kitten-with-blue-eyes.jpg";
document.getElementById("videoimgdiv").innerHTML = "<img onclick=\"doVideo()\" src=\"" + image + "\"/>";
}
</script>
<div id="videoimgdiv">
<img onclick="doVideo()"src="http://us.123rf.com/400wm/400/400/podlesnova/podlesnova0906/podlesnova090600034/5117393-small-red-furry-kitten-with-blue-eyes.jpg" />
</div>