You generally can not use the laptop screen as a second screen for the desktop. The HDMI/VGA port on a notebook is an OUT, not in.
You may be able to use software to let the desktop control the laptop, this makes it work like a second screen, but it will be doing all its own work.
Check this out. May do just what you need.They have other software to do the same thing.http://www.howtogeek.com/73603/how-to-use-a-single-mouse-and-keyboard-across-multiple-computers/