The latest Cygwin update seems to have broken how I launch mrxvt... my shortcut no longer worked. I tried countless permutations and nothing helped. After a lot of searching, I found that back on February 21, 2007 Angelo Graziosi posted a solution to the Cygwin mailing list that works for me (Hooray Google! Hooray Angelo!). His instructions were for launching urxvt, but I've brought them up to date and modified them for mrxvt.
First create a shell script. The one I created was named /usr/local/bin/start_mrxvt.sh
#!/bin/bash export DISPLAY=:0 /usr/bin/checkx || startxwin exec /usr/local/bin/mrxvt -e /usr/bin/bash -l
Next, create a shortcut to run the script with the following parameters
Target: C:\cygwin\bin\run.exe -p /usr/X11R6/bin bash --login -c /usr/local/bin/start_mrxvt.sh Start in: C:\cygwin\bin
This method works especially well because if X isn't already running, the script will start X before running mrxvt.