Paths which are fed to the JVM as parameters are switched to Windows format using cygpath, but $JAVA_CONFIG_DIR seems to have been forgotten. This results in an error during bootup:

Unable to read the logging configuration from 'file:/cygdrive/c/apps/jboss-7.1.0.Final/standalone/configuration/logging.properties'
(java.io.FileNotFoundException: \cygdrive\c\apps\jboss-7.1.0.Final\standalone\configuration\logging.properties (The system cannot find the path specified))

Fix:
This line needs to be inserted after line 157 in standalone.sh (inside the if $cygwin block)

JBOSS_CONFIG_DIR=`cygpath --path --windows "$JBOSS_CONFIG_DIR"`

The same bug seems to be the case for domain.sh.