If your computer is not loading the UI elements of the unmodified game, I don't think it'll be able to load modded UI elements. You can give something like EUI a shot, but I doubt it'll fix your problem.
The interference need not be something malicious, either. It can be something as innocent as an unstable voltage rail in your machine causing certain memory patterns to be loaded incorrectly. It can be a Windows library that got corrupted through some means and its most observable effect is that it stops Civ5's Lua code from behaving properly. It could be your installed copy of Visual C++ 2008 redistributable (that is necessary for the game to work) becoming corrupted and stopping Civ5 from behaving properly. There is such a wide pool of possibilities that it's impossible to determine which one it would be without further digging. The nuclear solution of reinstalling Windows tends to address a significant portion of this pool, but if you don't want to resort to that, you'll need to think back to all possible changes that were made to your computer (both software and hardware, and this includes potentially hidden updates) since the last time Civ5 worked and the first time you encountered this bug, eliminate changes that could never have an effect on Civ5 (e.g. updates that don't touch the core of your machine's functionality), and slowly whittle your way down the list manually until you end up fixing the issue.
However, this really isn't a Civ5 bug anymore, at least not a bug that can be fixed by people with access to Civ5's code; it's your specific hardware/software setup interfering with the execution of secure UX code, so unless that hardware/software setup is extremely common, it isn't worth my/our time to try to help you fix it.