However...
This was going nowhere, and, after about half an hour of struggle, I asked my mum which way the mouse was in her hand. She had the 'tail' coming out the back, which made sense to her.
Before working this out I was wondering if the light from the window was making it through the flimsy plastic of the mouse, to prevent the sensors from working. Or maybe something else was plugged in, robbing the MS-DOS PC of enough interrupts. Or maybe the ball was clogged with cat hairs.
We got there in the end, however, it was a lesson in not jumping to conclusions. I had just been temporarily defeated by my mother's lack of computer literacy.
It made so much sense that the very first computer mouse had the cable there, which is was why the device was initially nicknamed a “mouse”. They soon moved the cable to be more out of the way, but the name has obviously stuck.