I am going to tell you how to add or enable the "New" menu and "New Folder" option back into Desktop and Explorer context menu. So if you are also facing this problem, follow these simple steps to get menu option back:
1. Type regedit in RUN dialog box and press Enter. Now go to following key:
HKEY_CLASSES_ROOT\Directory\Background\shellex\ContextMenuHandlers\
2. Now create a new key "New" under "ContextMenuHandlers" key.
3. Select "New" key and in right-side pane, set the value of Default to:
{D969A300-E7FF-11d0-A93B-00A0C90F2719}
4. Close Registry Editor and you'll get the missing "New" option back in context menu.
PS: If you don't want to modify the Registry and want a ready-made Registry script to do the task automatically, download following ZIP file, extract it and then run the extracted .REG file: