Further to the post below, I decided in the end to go with a new iPod rather than a Zen. I'm still angry at Apple, but research suggested that both were similar in terms of lousy customer service, susceptibility to breakdown and pathetic warranty cover, plus a) the Zen has an apparently easily-lost connecting device, and b) I'd have to start all over in terms of buying compatible accessories.
Anyway, I opened up the box and had a look. There was something a tiny bit different about the new one-- like they'd redesigned it slightly. And indeed, they had. Including....
...the data port. The wretched data port which was the thing which eventually scuppered the first iPod. They redesigned the very thing that I'd found such a problem.
Thing is, I don't normally buy products which are fresh on the market; I usually wait until the kinks have been worked out, but somehow I seem to have gotten, well, a kinky one. I suppose in this case, I assumed that since Apple have been manufacturing these things since the 1990s, they'd've sorted out the obvious stuff. Anyway, things are looking better, but I'm still pretty miffed.
Update: Showed Alan the new machine, and he remarked that probably the reason Apple refused to fix the first iPod was because they'd been inudated with defective data ports and didn't want to go to the expense of replacing them all. He's probably right.