Sounds like something has disabled the right click from the group policy editor.
Go to Run, or the Start search box and type gpedit.msc, then User Configuration - Administrative Templates - Windows Components - Windows Explorer. In the right hand pane, scroll down to "remove Windows Explorer ’s default context menu”, open its properties by double clicking it. It may be enabled or not configured, disable it and you should find the right click facility will be back.
If you are using one of the "Home" versions of Windows 7, you will not have access to Gpedit.msc. The you may have to edit the registry.
Again, type regedit in the Run or the Start search box. Go down to HKEY_CURRENT_USER - Software - Microsoft - Windows - CurrentVersion - Policies - Explorer. In the right hand pane find “NoViewContextMenu”, set its value to 0 (if it exists).
If you still unable to right click the desktop, then find the same key here (again - if it exists): HKEY_LOCAL_MACHINE - Software - Microsoft - Windows - CurrentVersion - Policies - Explorer
The change, if you have not accidentally caused it yourself, is most often caused by a virus or trojan. I would suggest you do a full scan of the computer.