Rooting Galaxy S3: Entry in device manager not found when entering download mode
I managed to get it working using Windows 7 to root it. (Following the step-by-step guide without modifications). 

The order of things I tried in windows 8.1, each time attempting the rooting process:


Swapped USB ports
enabled developer mode
enabled USB debugging mode
Reset everything to factory settings
Swapped USB ports
enabled developer mode
enabled USB debugging mode


And I had repeatedly re-installed device drivers using Samsung Kies 3 during the above. Nothing worked. So maybe it's just windows 8.1 that stopped things working.