First of all, congrats on having the iPod nano for so long! I had one myself for about a year before I lost it and haven't found it since... I see your iPod won't charge. First off, how long ago was the issue of it not charging? Was it a few months, or a few years ago, or was it directly after you fixed the issue of it not playing music? If it was directly after, then you may have broken something and may need to get it fixed. If it was a while after fixing the music playback issue, then as simple as it may sound, it may just be a clogged charging port. On my Samsung S7 Edge, it seemed to have a loose headphone jack that would work, but the headphone cable would fall out and would not stay connected in the phone. At first I though I broke it, but after wrapping some double sided tape around a paperclip and cleaning it out, not only did I find a ton of dust, but it worked normally again. So, that may be the issue. If that does not work, my only other idea for its issue may just be a broken charging port. You clearly have used it for the many years you've had it may have just worn the charger until it finally gave out. If you believe this is the issue, here is a link to the tutorial on how to do it (I could not find any logic board replacements because the nano is a rare sight nowadays so I only included the tutorial on how to replace it). Although, just a fair warning, the charging port is connected to the logic board meaning you will have to replace the logic board of the device, which erases everything you have had on it, but can be downloaded again in the iTunes store. Lastly, if the repair looks too difficult, or you cannot seem to find a logic board replacement from a legitimate sight, then you could buy a new one for less than $100.
Hope this helps!
Tutorial: iPod Nano 6th Generation Logic Board Assembly Replacement
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