Can't say I have, but just to get all the support flowchart stuff out of the way: You've got the correct logitech driver software installed as well as everything plugged in right?
If the GT's anything like the G27, you might have had the power brick slide out just that tiny part to not power things.
ALSO! I'm taking suggestions for the next week's league, as much as I wanted to take part in this week's one, I can't get my racing sim setup where I am right now. So yes, do please say what your favorite stages to tackle are, and what class you want to try out with against everyone here.