In other other news... what the... life just got even more interesting.
On a whim, I tried plugging in my usb game controller.
And it... works...?
It can't just be my mouse, because my mouse works on other computers. Same with the other USB mouse I've tried.
Apparently this is more complex than just "external hard drive good, devices bad."
How very strange... I must investigate further.
Ideas? Delighted. But lost.