Just an update: this issue still persists. I've tried two different hubs, two different USB cables, and two different Pro Micros. Behaviour is still the same:
1) Plug arduino into powered PC: detected and works fine immediately.
2) Turn PC off
3) Turn PC on: arduino not responding to inputs, one LED shines for power but none for RX/TX or any other behaviour
4) Unplug arduino
5) Reconnect arduino to PC: detected and works fine immediately.
Does this sound like a power issue, or a question of drivers? I've even reinstalled the PC from windows 7 to windows 10 and reinstalled the IDE to a newer version, but nothing's helping.