177 UDP is for XDMCP, right?
If you can login through putty, and have X forwarding on, you could start X applications when you have the cygwin/X server running.
If you desire a whole X environment with an X manager like KDE, you could consider using 'startx' to have the X session start through the tunnel.
If the putty tunnel is not desirable but you want a desktop environment from the linux box, you should reopen port 177 to allow xdmcp again.
I personally have the cygwin/X server running all the time, patiently waiting for connects, and I have set up putty to do X forwarding. When I log in to my router / server, and start some management tool requiring X (Fedora, duh), it just pops on my screen without hassle.
Hope this helps..