Lionclaw, Dread Knot, Oleander, Skybird...great ideas and links, thank you all.
Hinrich Schwab...believe it or not, I stumbled into an apparent solution to almost all the problems.
I reinstalled TC2M, using the standard "trick" to create a root folder outside of the Program Files/Program Files (X86) folders.
Then I
forgot to open the executable's Properties and select "run as XP" in Compatibility Mode. I clicked the desktop icon and the darn thing opened and ran in full-screen. I even managed to guess at the location of the cursor and closed it successfully, no more endless theme music or "dithering" Windowed-mode screen! Perhaps the machine is smart enough to know how to run the program without silly user interference to tell it how to do its job...strange.
So, the only problem left, I hope, is that disappearing cursor. It is visible on the task bar down at the bottom of the screen (I keep that locked on top of all apps), but as soon as I move it off the task bar, it disappears behind the game screen and you really can't play by guessing where the darn thing's at.
If you can give me a hint at how to fix that, I'd really appreciate it!