Hi, it sounds like you are doing everything correctly but that there is a problem with your compiler setup inside Cygwin.
Could you try first compiling a basic C++ program (just a main that prints out "Hello world") and running that to see if it works? By basic I mean not including any of ITensor in your program. Also try including something from the C++ standard library, such as making a std::vector to make sure that also works.
That could help clarify what is going on. From the error message it sounds like you might need to uninstall Cygwin completely and reinstall it.