Thanks to Sparx for all the effort. I have a horrible feeling that I've picked up something horrible like the "wrong" Midi.h file, or perhaps there's something in this PC which hates libraries.
I have all the Arduino source files and libraries on my C: drive, and all the sketches on a separate hard drive, which I've heard is a fairly normal way to arrange the Arduino world.
Otherwise, I am in the lap of the gods, and it is not a good place to be. I've got all the upper- and lower-case issues out of the way, and there is no spitting back about missing any of the libraries.
Is there an official Midi library that comes with the IDE? I only ask, because the errors, in my head, seem to point to this library as being the weakest link, and I seemed to get directed to a gihub repository for it; who knows what sort of mashing it has had in there?