No, it would be powerd by the PC - but when the PC is off then it wouldn't be providing power anymore. It was a bit off topic, so ignore it.
If you can get your hands on a patch cable, try it. Sometimes the solution is as simple as that.
Check your Bios settings for the laptop to make sure the ethernet port is enabled.
Apart from that, I would start looking at the usb device, which I'm sure you've done though
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