Taking a look the reason is because you need a full site URL. You have:
templates/bigpicture/images/background.png
So on your sub pages its actually adding in the whole url here:
http://209.236.117.153/~devachungo/index.php/extensions/s5-accordion-menu
This is why the image isn't showing. Just enter in your full URL which would look like:
http://209.236.117.153/~devachungo/templates/bigpicture/images/background.png