The Facebook Connect API comes packaged with the JSON wrapper (an easy to use mechanism for transmitting data between two servers). The error indicates that something else in your system is also trying to include a JSON class with the same name, so PHP doesn't know which one is the correct one to use.
Not a permanent solution, and may cause issues, but you can rename the JSON file below to see if that fixes the issue. This will cause the FB API to use whichever one is installed already, which may cause incompatibility issues.. but at least will help you figure out if it works.