Why are the files on the desktop? iTunes should be ripping the files to <User's Music>\iTunes\iTunes Media\Music\<Album Artist>\<Album>\## <Name>.
Perhaps you have a permissions issue and it can't move the files it wants to.
Right-click on your main iTunes folder and click Properties, then go to the Security tab and click Advanced. If necessary grant your account and system full control to this folder, subfolders and files, then tick the option to replace permissions on child objects which will repair permissions throughout the library. This is the XP dialog but Windows 7 shouldn't be too different.