We have CS6 running on Windows 7 Pro 64-bit. We purchased ITC Zapf Dingbats Std from Adobe and installed them on the PC. It shows them in listed as installed and if you try to reinstall them, then it prompts and says they are already there. Our issue revolves around using them, when you use them in a current or new document it only shows a box with an X in it and not the font. What is the fix for this issue? As a side note, we also had purchased several Helvetica fonts and installed them without issue and they work without any issue.
What do you see in Story Editor if you switch to that view?
Are you typing in text from your keyboard? Try inserting a character through the Glyphs panel.
The old way of adding dingbats and other symbols to a font was to substitute regular characters with them, so to get a fleuron, you'd type something like a "D" and rely on the font encoding to get the "right" character. With modern fonts (and modern versions of classic fonts), that practice has been deemed obsolete and not interchangeable. To insert a dingbat, you'd need to type the actual character on your keyboard (and you are unlikely to have a "five point white star" key), or insert the appropriate code otherwise, such as through the Glyphs panel.
The Adobe Font store does report the character encoding for Zapf Dingbats as "Symbol/Pi": http://store1.adobe.com/type/browser/info/charsets.html#symbolpi