Indesign interface in Italics

I'm not sure how you know that the new fonts that you've downloaded are not the problem. Unless the fonts that you're referring to are Adobe fonts there very well could be a font conflict depending on where the new fonts came from. You said that you're using CS6 but you did not say what operating system that you are using. On a Macintosh the default interface font has changed several times over the years (Chicago, Charcoal, Lucida Grande, Helvetica Neue and SF Pro have all had their day) so maybe your new fonts are any of those.

With the possibility that the problem is not related to your fonts in mind try trashing your InDesign caches. This process is not the same as trashing preferences and is more specifically intended for fixing problems with the interface.

To trash InDesign caches:

For Macintosh Users: The User Library folder in which InDesign’s cache files are stored is hidden by default on most Macintoshes. To access it make sure that InDesign is closed and click on the desktop to launch a Finder Window (Command-N). With this window in column view follow the path User>Home folder (it’s the folder with an icon that looks like a house—it may have the user’s name rather than “Home”) and click on the Home folder. With the Option Key pressed choose Library from the Finder Go Menu. “Library” will now appear within the Home folder. Within the Library folder find the “Caches” folder. Within the Caches folder find and delete the entire folder “Adobe InDesign”. I find that deleting the InDesign cache folder completely leads to a lasting change.

For Windows Users: On Windows 7 and above the caches files are hidden. To find them go to the Control Panel and open Folder Options and then click the View tab. Then select “Show hidden files and folders” or “Show hidden files, folders or drive options” in Advanced Settings. Then delete (or rename) the folder at the end of this path: C:\Users\[User Name]\AppData\Local\Adobe\InDesign\Version [#]\<Language>\Cache.

Trash your preferences. Beyond that you need to realize that software is 13 years old and unsupported under any modern operating system. I do not recommend uninstalling as there's no telling if you'll be able to reactivate it.