Hello. My name is***** can help you with your question.
The first thing I would do is switch it out of disc mode again to see if you can get recognized. I would restart the Mac after that, and then plug it into a different USB port. This should cause your computer to recognize the device and install the driver forward again. If it doesn't then it may be a problem with the iPod classic. If that's the case, let me know and there are some other steps that we can take.