Sounds very symptomatic of a nasty bit of spyware called Smitfraud. Try this anyway and see what happens. Its worth a try and wont harm your system any further even if it doesnt work...
First of all download the program SmitRem.exe by clicking this :
http://noahdfear.geekstogo.com/click...click.php?id=1
Extract the 4 files and then run the file RunThis.Bat file by doubleclicking it. When its gone through, reboot and see if you can right click on ya desktop again and re-tick the show desktop icons option.
If that doesnt make your icons come back or you still cant right click after running SmitRem and rebooting, try going to this site :
http://www.kellys-korner-xp.com/xp_tweaks.htm
Go down the page to line number 128 and on the right hand side you will see an option for Restore Desktop and Screensaver tabs. Just click it, click Run and say yes to the registry alteration then fingers crossed you will be able to right click on the desktop once more..
If none of this works - let me know...
Jimbo T

blower