Here is my contribution to this debate. I have no solutions, but I do have some slightly more detailed diagnostics.
As a family we have 3 computers (all running OS X 10.4.2) and 3 ipods (1 3G, 2 4G). One of the 4G iPods developed a fault (under warranty) and has just been returned from Apple repair (since there are no scratches it looks like a new iPod). My daughter found immediately that when she plugged it into her computer, it didn't show up.
So, with more than one computer and one iPod. I could do quite a few tests.
The problem exists for one specific iPod (the repaired one) and one mac (a Quicksilver G4). The one specific iPod has no problems with the other two macs (one powerbook, one dual-G5). The one specific mac also has no problems with the other two iPods (one of which is an identical model). It really does look like a specific computer/iPod combination.
This specific computer/iPod combination looks okay using the USB connectivity (although the computer only has USB 1, so it isn't a great alternative).
So what happens when we use the faulty computer/iPod combination? The iPod is not seen on the desktop, iTunes or iPod updater. But, when I run the system profiler it is seen in the FireWire Device Tree as an iPod. However, if you know how the report should look, there are 4 layers of detail. Usually you get the layers iPod: > iPod Unit: > iPod SBP-LUN: > "My own iPod name". Under each layer you get some information, down to information abut the Mount Point. The interesting thing is that when I use the faulty computer/iPod combination, and run system profile, the report on the iPod un the FireWire Device Tree only reports down to the heading for iPod SBP-LUN:, but reports no information for this layer not for the fourth layer.
I have tried various tricks, such as resetting/reinstalling the iPod software on one the computers it works with, and playing with the trick of putting into disk mode and back again (both plugged in and unplugged). With regard to setting the iPod into disk mode, when I do this, the computer still doesn't see the iPod as a disk on the desktop. I have also tried resetting the firewire bus by switching off the computer for some time, but I don't believe the fault is with the firewire bus specifically because other iPods work with FireWire as do other devices.
So, it really does look like a computer/iPod combination, as at least one other person has suggested. But I have no idea of what to do next!
I should add that I have looked at both
http://docs.info.apple.com/article.html?artnum=60950
and
http://docs.info.apple.com/article.html?artnum=61937
But neither really help. I noted the advice to reinstall 10.4, but haven't tried that one. Perhaps I should, but given that other iPods work with this computer, I am not sure about this.
I hope this level of detail helps in the discussion.