Can't mount/access iPod on a computer

I'm trying to help a friend who has a problem with her HP iPod (basically the same model as a 40GB 4th Gen Clickwheel). The About screen says that there are 3071 songs and that the capacity is 37.1 GB with 37.0 GB available, so obviously something is screwed up there. But everything works fine in terms of navigating through the menus, playing and other manipulations of the songs and podcasts, charging via USB and Firewire wallwarts, and the battery holds a good charge. The big problem is when the iPod is connected to a computer (either Mac or Windows) the hard drive goes into a clicking loop and cannot be accessed. The computers seem to know it's connected, but the drive won't mount - it doesn't show up in macOS Finder, iTunes (Windows and macOS), macOS Disk Utility, etc. I also tried the Mac version of the EaseUS recovery app to no avail. I even purchased an external enclosure for the hard drive and tried connecting it that way but got the same result. Same with putting the hard drive into other known working 4th Gen iPods: everything is navigable and playable via the iPods, but connecting to a computer is a no-go. Of course, there is no backup copy of the iPod's music library on any computer, so we really want to try to retrieve all of the music and podcast files from the iPod itself and reload them into a fresh iTunes Library - something I've done before with other iPods, so I think I know what I'm doing.

Does anyone have any suggestions for how I might be able to get at the contents of the iPod's hard drive? (BTW - it is formatted for Windows.) I suppose the last resort is to hire a professional data recovery service, but I hope to do it myself and avoid that expense.

Thanks in advance for any suggestions you can offer.