The unit predates modern models and is out of usual range of official support by several years.
No parts, and beyond official Apple repair. Have you sought an independent authorized repair
facility to ask if they could even get parts outside the official stream to try & fix your antique?
..Looking back, I see a few instances of that HP-sponsored model online. From some time ago..
{Even four years ago, the HP links to their support failed to function. Not sure why Apple's should.}
Pingback by Today in Apple history: HP’s iPod comes out of the blue — January 8, 2018 @ 2:17 pm
Some may view such an item as collectable; however unless as-new in original packing, in mint
condition, it may not be worth all that much. Parts from a non-HP model may swap out OK.
Tested and Works Great. **Please note, these iPods are very old, and we do not guarantee
the battery** The battery is tested to accept a charge, and everything else ...
rover.ebay.com/rover/1/711-53200-19255-0/1?icep_ff3=2&pu...
Neither Hewlett-Packard ... Congratulations on purchasing your Apple iPod from HP.
Read this section to get started using iPod quickly. iPod works with your PC.
h10032.www1.hp.com/ctg/Manual/c00310611
I checked HP and their links for the hp ipod don't work anymore
https://discussions.apple.com/thread/5861155?start=0&tstart=0
The agreement would produce the "Apple iPod by HP ... The only noticeable differ-
ence (apart from the box it came in) was an HP logo *** "invent" motto on the back.
storiesofapple.net/the-apple-ipod-by-hp.html
Sorry to be unable to help you in this matter.
Good luck & happy trails! 🙂