This error message means that Windows isn't able to find "cygwin1.dll". The Programs that the Cygwin gcc create depend on this DLL. The file is part of cygwin , so most likely it's located in C:\cygwin\bin. To fix the problem all you have to do is add C:\cygwin\bin (or the location where cygwin1.dll can be found) to your system path. Alternatively you can copy cygwin1.dll into your Windows directory.
There is a nice tool called DependencyWalker that you can download from http://www.dependencywalker.com . You can use it to check dependencies of executables, so if you inspect your generated program it tells you which dependencies are missing and which are resolved.