Looking at you log, you system is no longer infected but the desktop was disabled.
First, go to run and type explorer.exe and click ok. It should restore the desktop. If that does not work...
Open your registry editor (run regedit) and search the following key
HKLM\...\policies\Explorer] - "NoActiveDesktop"=1
Change the "1" to 0 and reboot your machine
If the above does not recover the missing icons, you will need to restore the system.