My system hard drive icon has disappeared from my desktop.

First, double check Finder>Preferences to be sure Show Hard disks IS checked.

The drive may have an incorrect visibility setting.

Native Instruments users can download a script to fix that setting at:
http://www.native-instruments.com/knowledge/questions/165

Other’s can follow these instructions:
Launch ScriptEditor and copy and paste this into the script window:

tell application “System Events”
set visible of disk “NameofDisk” to true
end tell
tell application “Finder” to quit
delay 1
tell application “Finder” to launch

Replace NameofDisk with the actual name of your disk, hit the Compile icon to make sure the script didn’t acquire any errors, and then hit run. This should set the visible attribute back to visible and quit and relaunch the Finder, thus making the change available.
(http://www.pinkmutant.com/articles/invisible.html)

Knowledge Base