Cygwin install instructions
The default install of cygwin does not install the necessary files to
fully run an X server to allow you to display remote X applications.
After you download and run setup.exe from the cygwin link, you will be
prompted for a location to install, and then you will select a mirror
from which to download. Afterwards you will see a screen which asks you to select the components you wish to install. It looks like this:
Scroll down to find the X11 category and click the word Default next to it until it changes to
Install
...then continue with the installation. This should install all the X11
components you need for a functional X server.