And I learn something new every day :-) (didn't know about gij). Thanks! This is the right list. As for a working Java on the machine, you should probably use gij (part of the gcc-java package), and just have a dependency on that package, rather than trying to use a non-cygwin non-free VM (are there any other open source VMs ported to cygwin yet?).
You may also want to read up on http://cygwin.com/setup.html.