Q: Desktop Icon Deleted!!

That would be expected....since the folder Desktop is only accessible to the user who owns it and nobody else has permission....which is why the last command would modify the permissions of desktop folder correctly > set ownership for the Desktop folder to your account with the proper ACL configuration (600).

yeah your going to have to force remove that via the terminal.

sudo rm -rf /path/to/desktopfolder

This is makeshift solution and reinstalling the 10.8.4 combo update would fix your problem.

Why don't you reinstall the OS.

Ciao.

That surprises me that an OS reinstall fails to solve the issue.  I would take this to an Apple store.  The technicians at the genius bar probably will not be able to solve this issue (they are principally hardware oriented) but they may be able to escalate this to some software specialists.

Ciao.

Your problem may seem trivial because it does not prevent you from using your MBP.  But a reinstall should result in an OS exactly as you had it earlier.  It may very well be minor but it could also be a portent of other issues.  Thus from my perspective, this is a legitimate item that warrants examination and correction.

I note that on your profile you indicate that you are using 10.8.2.  Have you installed 10.8.4, the latest version?

Ciao.