The files that do compile are on your system path, so the compiler can find them. speech.h isn't, so you have to tell it where to look:
g++ -c test.cpp -I<Path_to_speech.h>/speech.h ...
I.e. if it's in C:\Users\Kirk\test\include
, then
g++ -c test.cpp -IC:/Users/Kirk/test/include/speech.h ...