I searched the net to find out how to change the computer logo icon, in the GDM-3,login box,and found nothing. I have Pinguy 12.04 installed as my O.S, which is based on, Ubuntu 12.04 .I have Cinnamon
installed as my Desktop So I made my own fix.
Here is what I came up with.
Unzip the file,and place it in user/share/icons file
Then go to your menu and find, GDM3 Settings and change the icon theme to GDM-Logo-Icon
I hope this helps someone.
If you want a different icon just replace the .PNG file with your own. Just make it the same size.