My understanding is that the shoutbox works by creating a new thread in a hidden forum that you create when installing it. (All permissions are set to No Access).
Go into the Admin section,
Forum Management panel -> Edit or Delete Forum then select shoutboxpal (or whatever it was called when created). There you can change it so that Admin has read/write access.
Confirm the new settings then go back to your main page the forum is now listed there. It'll show 0 threads with 0 replies, don't worry about this, when you open it you'll see each post appears as a thread. Open the offending post/thread and you should see his/her IP.
