Hi,
Norton Internet Secruity comes preinstalled on many Branded computers such as Dell, HP etc, so its not that in installed itself.
Since it fails to get uninstall from add/remove programs run the link below and it will completly remove the norton product from your computer if the icon remains then simply right click on it with mouse and delete it
www.symantec.com/nrt
once ur issue is resolved pls reply and close this thread as solved, if not then pls give details about what happened with u ran the tool from above link
thanx