Before running jetty-cygwin.sh on cygwin, define the JAVA_HOME and JETTY_HOME first.

$ export JAVA_HOME=/path/to/jvm
$ export JETTY_HOME=/path/to/jetty

Examples:
$ export JAVA_HOME=/usr/bin/jvm
So assuming you installed cygwin on C:\cygwin, the jvm needs to be in C:\cygwin\usr\bin\jvm

$ export JETTY_HOME=/usr/share/jetty6
So assuming you installed cygwin on C:\cygwin, jetty needs to be in C:\cygwin\usr\share\jetty6