hi, i can not help about the cygwin thing,
still i think that you first should confirm that processing-java works.
- so when you say
I’m in the correct directory.
again, open a cmd window there?
yourdrive:/…/processing-3.4/
check with dir
that you see
processing-java.exe (26.07.2018)
and type
processing-java --sketch=yourdrive:/../processing-3.4/modes/java/examples/Basics/Image/LoadDisplayImage --run
it works here / win 7 / but full install processing 3.4 IDE