I've spent as much time bashing companies' customer service as the next guy, so I figured I'd post and let people know how it all turned out.
Apple promised to send a new iPod and took my credit card # as guarantee that I'd return the defective one. What they sent us was an iPod dock, which solved nothing. I called Apple and explained and they asked me to send it back when I got around to it, but they'd have an iPod to me within 2-3 business days. This was yesterday. About 30 mins ago, the new iPod arrived with a return label so I wouldn't have to pay to return the defective one. Never been an Apple customer before in my life, but I'm pleased with their overall service in this case.
Gotta give credit where it's due.