Hi, are you missing just desktop icons or desktop and start menu icons? Some viruses set all these to hidden to try and keep you from your anti-virus program, my parents got infected by one.
To see if they are just hidden and not deleted try this:
Right click the Start button and select Explore All Users.
Look for an icon on the left panel that says Desktop, click it.
Now at the top of the window click Tools and Folder Options.
Click the View tab.
Scroll down to Hidden Files and Folders
Click the bubble that says Show Hidden Files and Folders.
Click Ok.
Did the Icons come back but semi transparent? If so right click on the files and hit properties
Uncheck the Hidden box and click OK.
Once you have restored all the files back to their normal state you should probably change the folder options back to hiding hidden files, most files are hidden for a reason. Also run an up to date antivirus program immediately.