AHA!!!! That's what it was.
Just a few days ago I had downloaded and installed the Remove Shortcuts from Method 1.
Then yesterday when I installed iTunes I was rebooting the computer for the first time in a while so I incorrectly blamed iTunes when in fact it was Method 1 in this link: Shortcut Arrow - Change, Remove, or Restore
that for some reason left the icons the way they were.
Now I just downloaded it again and clicked the "Restore Arrow" and after a reboot there it was.
By the way in Method 2 i got an error message before "Log Off" that's why I tried No 1.
Thanks A LOT to all of you for your help