pwd is commonly both a shell built-in command and a standalone executable, provided by GNU coreutils (which Cygwin installs by default).
If you're invoking make from the Cygwin environment (say, typing make at a bash shell prompt), then C:\cygwin\bin is the wrong way to specify the directory. That's the path as seen from Windows. From within Cygwin, it's /bin -- and it should be in your default $PATH. The Cygwin equivalent of C:\MinGW\msys\1.0\bin would be /cygdrive/c/mingw/msys/1.0/bin
If you're doing this directly from Windows rather than in the Cygwin subsystem, then C:\cygwin\bin is the path to the Cygwin bin directory -- but running C:\cygwin\bin\pwd is going to give you a Cygwin-specific directory name that's not going to be meaningful to Windows.