It seems there are some validation issues with the site code that may need to be addressed first, though you might not have to resolve them to successfully troubleshoot the problem. You can see some of these by using validator.w3.org. Perhaps updating your theme and plugins to the latest versions will correct some of the issues, but it might be necessary to dig into the code directly to get things lined out.
That being said, the typical cause for RPS Image Gallery not functioning properly is that fancybox is not able to load due to a JavaScript error higher up on the page or the fact that another version of fancybox is loading from another source.
You may want to try and find out if the compatibility issue is between RPS Image Gallery and your theme or other plugins through the process of elimination. It takes a little time but can be as easy as disabling all plugins except for RPS Image Gallery, then seeing if problem persists. If it does, then that would be a good indicator to reach out to the theme developer for support. If not, then you would need to activate plugins one (or a few) at a time until the problem resurfaced.
We hope this information helps in your efforts.