In addition to a new retropie case, I also got a new turbo controller from Amazon. Sadly it did NOT work on the Xbox 360 but I will try again because it is working great on the Retropie now that I've got a Final Fight game going and have mapped out the controller. I also managed to get the turbo button to work as well. I'll just keep it with my retropie gaming system for now:
Basically it's looking like my Xbox 360 is strictly "Xbox 360 products ONLY" at this point. This is kindly why I got into the retro gaming world with the retropie system. As long as it's equipped with and operates off of a USB cable, I can use it on my retropie.