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Nope, it's currently not possible to statically link against cygwin1.dll; if your application does not use unix emulation (i.e. pure win32) you can pass -mno-cygwin to the compiler.
See also the FAQ:
http://cygwin.com/faq/faq.html#faq.programming.win32-no-cygwin
http://cygwin.com/faq/faq.html#faq.programming.static-linking