Desktop icons missing

What with?

Are you meaning you ran an Anti-virus scan, or did you run a Clean-Up scan, or what?

If you ran a 3rd party utility scan, does it not have a capability to restore what it removed?

Right click desktop > View > Ensure 'Show Desktop Icons' is checked if not click it.

If it is checked marked, go to recycle bin and look for them there. If you used a Disk Clean up or a 3rd party tool to remove them, and they are not in the Recycle bin, then you will have to go to every program in the all programs or through My Computer to the actual directory and right click program file > send to desktop as short cut.

If you find anything with these tools, turn off System Restore and run them again in Safe Mode

Download Spybot - Search & Destroy and install it. Update it. http://www.safer-networking.org/en/download/index.html

Download Malwarebytes Anti-Malware, install it and update it.

Malwarebytes

* Double-click mbam-setup.exe and follow the prompts to install the program.
* At the end, be sure a checkmark is placed next to Update Malwarebytes' Anti-Malware and Launch Malwarebytes' Anti-Malware, then click Finish.
* If an update is found, it will download and install the latest version.
* Once the program has loaded, select Perform Quick Scan, then click Scan.
* When the scan is complete, click OK, then Show Results to view the results.
* Be sure that everything is checked, and click Remove Selected.

If you encounter any problems while downloading the updates, manually download them from here and just double-click on mbam-rules.exe to install.
mbam-rules

I would keep scanning with it until it is clean by closing out and rebooting and running it again.

Run this Rootkit Revealer GMer
Gmer

When your infected with any trojans, spyware, malware, they could have been saved in System Restore and can re-infect you. It's best to remove them.

XP
Press the WinKey + r type sysdm.cpl and press Enter.
Select the System Restore tab and check "Turn off System Restore".

Vista
Press the WinKey + r type sysdm.cpl and press Enter
Select the System Protection tab. Untick the box next to Local Disk C: and any other drives and click on Turn System Restore off.

After scanning the system and removing the offending malware, re-enable System Restore by repeating the steps, this time removing the check from "Turn off System Restore".

Let us know how you get on.