First, run the download / installer for Cygwin from http://www.cygwin.com/
When you get to this screen, wake up:
At this screen, scroll down until you can see X11.
Expand the X11 category by clicking on + and select the X-startup-scripts (there are two pictures in this document because you can't see the full name otherwise):
It might complain about dependencies, but just click Next anyway, and it will sort it out:
Then run the Cygwin bash shell, and run the X program. Here I don't happen to have DNS working, so I had to use an IP address. The -fullscreen option is rather cute, but you don't have to.
Then you'll get a graphical log-in prompt. The fonts are a bit off, but hopefully things will still work OK.
HP decided to put the button to run a terminal window somewhere obscure.
And you can use the window that pops up just like a telnet session, except that the DISPLAY environment variable is set correctly, and so forth.
