Maybe I'm reading it wrong - and if so, I hope you can tell me what I'm missing - but putting the iPod into Disc Mode seems to involve the reset working. When I try to do the reset - i.e. "Turn the Hold switch on, then back to off.
Press and hold the Menu and Select buttons for 10 seconds (until the Apple logo appears)" - I never see the Apple logo. It just goes to a black screen, then back to a white screen, then black, then white and on and on till I take my fingers off the iPod. Again, unless I'm missing something, putting it into Disc Mode seems to depend on getting the Apple logo to appear. I did charge the iPod for 3 or 4 hours after initial reset failed, and again could not get the logo to appear.
One other thing I did not mention as I was not sure the iPod was at fault. After successfully listening to a podcast in the car through the iPod, I tried to listen to a different one and it sounded like a 78 record being played at 16. I wasn't sure that is wasn't my download that was at fault until just now when I listened to it on my iMac. It was right after this, when I took the iPod out of the car, that I noticed the white screen.
One last thing. My iMac can see the iPod and the music tracks and podcasts it contains. I did a restore from the computer, but nothing changed.