Here are a few basic fixes:
Right-click on your Desktop and select:
Properties > Desktop > Customize Desktop > Restore Default
right click on the desktop, chose properties, go to the
desktop tab, click Customize Desktop... there you can
choose which icons you want to be shown on the desktop.
Start
My Computer
Right click, check "Show on desktop"
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As to your overall condition I would suggest:
please follow
owen's Instructions and then post your log in the
Spyware, Adware, Viruses and HijackThis Logs section (
Not Here).