Sorry for not being part of the discussion. I simply don't have time for WordPress development anymore. I just checked compatibility with WP 3.8 and updated the plugin.
As cazman mentioned, there were a couple deprecated jQuery features that I have removed from the plugin, though I doubt that was the cause of your trouble.
Now, to give a little explanation of how the plugin works: the Vertical and Cascade styles are put together by the server and then sent to the web browser. This makes them the most reliable options.
There are 2 reasons (that I know of) for why the plugin stops before putting together the display.
The easiest way to figure out if the problem is with the PhotoTile plugin, the theme, or another plugin is to use one of the default WordPress plugin (which are well written) and then enable one plugin at a time.
I hope that helps. There is definitely a learning cure to problem solving these things. One last thing I would mention is that you can listen to your browser and see if it announces any errors. Using Chrome or Firefox, go to your website, right-click anywhere on the page, and select "Inspect Element". A panel should appear at the bottom of the page. Select the "Console" tab and then reload the page.