Screenshot area to clipboard (Control + Command + Shift + 4) doesn't work
Things to check...


The receiving app can accept the format, .png by default.  
The buffer hasn't been replaced with other content, text etc.  
If  Cmd ⌘   Ctrl ⌃   Shift ⇧   3  would work to capture the entire screen to clipboard.  
That the key commands are on &amp; set to defaults in System Prefs > Keyboard > Shortcuts > Screen Shots &amp; also that resetting to defaults doesn't generate an orange warning triangle that another shortcut is using the same key command.