I don't know much about cygwin, but I'm not surprised you encounter a problem.... cygwin is already another layer of hacking complexity, ontop of win32..... apparently the dll you got has no compatible symbols to the win32 system you are using. Zinc has a win32 port on their website, that runs,(but I think they have minimum win32 level.... but I did get it to work on Win98 once ;-)

In other words...trying to get a fully functional bug-free zinc, by compiling under cygwin....is probably futile. In fact, under cygwin, I believe you would try to install the linux zinc version......what a nightmare that would be...on win32

The best place to ask this the Zinc maillist.... but don't expect to get help on any Zinc version on win32, except for their approved win32 binary download.