Tenacious Icon - Plz Help

Hi. I have a problem with a tenacious icon. Apparently an AOL icon was placed on my desktop when I installed something else. This is problem enough but unfortunately I can’t remove it! The regular methods for deleting an icon do nothing. Can someone please help me get this rotten thing off my desktop?

Thanks in advance for any help you can offer.

Is it possible the icon is saved in the All User folder and keeps replicating when you boot?

C:\Documents and Settings\All Users\Desktop

Or check what runs when you start up, maybe something hooked in to always test for that icon.