Download ShellExView here:
http://www.nirsoft.net/utils/shexview.html
Run it and follow these steps:
From the menu, click on Options then click on Filter by Extension Type and select Context Menu
On the list, you'll see some of the entries with pink background, those are installed by the third party software
Hold down CTRL Key and select all of them then click on the red button on top left corner to disable.
Click on the Options again and select Restart Explorer
Now try to right click on desktop to see if it fix your problem. If it does then start to enable one by one and repeat step 5 until the problem occurs again, that's the offending extension.