I don't use an X-Box but I use a G-27 on a PS4-Pro via DriveHub so I hope I could help you.
For us, we need to have a good quality micro usb cable that runs from the DriveHub into a DS4 Playstation Controller. The Controller MUST be set to off prior to plugging it in.
Now, I'm not sure if it works the same on your system but if it does I can not stress enough how important what I just mentioned before is to having DriveHub run stable.
There are countless posts by new DriveHub users who at first have issues like you, all to realize that it was either a low quality cable, or that they were plugging in the cable into a controller that was on.
So, a good quality micro usb cable and, to make sure your controller is off prior to plugging in the cable.
Hope that bit helps but if not, GTPlanets boards have a ton of info on this if you do a little searching.
Umm, I don't think he's going to need to run his G-27 via his PC mate. If he was running his G-27 on his PC then yeah, Logitechs software would come in handy. However, a PC is not necessary at all for DriveHub to run properly on consoles. Nor is a PC necessary to have a G-27 to run on a PS3 and obviously a PS4.
Keep us updated on your progress.