From what I can see, the problem seems to be linked to a translation plugin that you have installed. Not only is this plugin loading an older version of jQuery than the one that comes with wordpress, but it's loading it for every single Translation link that gets displayed on the page.
I would first try deactivating that plugin to see if the Modal Dialog window comes up. If it does, then you've found your culprit.
Then, you could try contacting the author of that plugin and asking that person to change their plugin to load WordPress' copy of jQuery only once in the page header.
Alternatively, I could look at making the change to the plugin you are using, but that will break on upgrade, and I would only have time to do this if the change is simple.
You could also see if there are other plugins out there that would do the same thing but without the jQuery conflict.