Went over to the Apple store this morning to see if they could resuscitate my dead iPod. They couldn't, but they gave me a new one and charged it as a "repair" rather than a replacement, which meant that it cost me slightly less than half what I was expecting to spend on a new iPod today. So, I'm glad I went to the slight extra trouble of bringing it in for service rather than just buying a replacement.
I'm just hoping that this latest regeneration* of my 160GB iPod Classic proves more durable than the last two. Every other iPod model I've owned has survived years of hard use. This one's been replaced twice in 18 months for hardware faults of various kinds. Unfortunately, there's not much competition in the "I want a device that just plays music and holds a ton of it" market, so I don't know that I have a reasonable alternative.
*And yes, my iPod is now officially named "Pertwee". Thanks, brain.