Semper Fi, Mac. (Somehow, that seemed appropriate here.)
Anyway, what you can try to get maybe a hint is to do a verbose boot by holding down the cmd-V combination when you power up. This switches part of the boot process from the gray Apple screen to a black Unix terminal screen where a lot of text output is sprayed out reporting what is going on. This you should be able to ignore. On the backside, when you command a shutdown, you should eventually get to the same kind of screen, which will probably show some process refusing to be killed or the machine waiting forever for something to happen.
You can make this the default boot mode by opening a Terminal session using /Utilities/Terminal application, then typing the following command at the prompt:
sudo nvram boot-args="-v" <enter>
Terminal will ask for your password to authenticate you are doing something with admin privileges, and you should be good to go.
If you later want to undo this, you can do that in terminal with the following command:
sudo nvram boot-args="" <enter>
This also will ask for the password before proceeding.
Anyway, I don't know what specifically will show up on shutdown, but you may get a valuable clue.
