The iPod Shuffle 4th generation is impossible to take apart without destroying it. You’d be better off buying a new iPod on eBay. New condition: https://www.ebay.com/sch/i.html?_dcat=73... Used or refurbished condition: https://www.ebay.com/sch/i.html?_dcat=73...
Make sure you’re using a 30 pin dock connector to FireWire cable to charge it, not a USB cable. While this iPod has a dock connector, it can’t charge through a USB to dock connector cable like the other iPods. You will need the cable and the power adapter. Cable: https://www.ebay.com/sch/i.html?_from=R4... Power adapter: https://www.ebay.com/sch/i.html?_from=R4... Note that some eBay listings might contain both the cable and power adapter.
Sounds like the hard drive is dead. You will need to replace it, either with another hard drive, or with a compact flash card or SD card using adaptors like these: https://www.iflash.xyz Here’s the repair guide: iPod Classic Hard Drive Replacement
(1) Charge the iPod for a few hours. (2) Try resetting the iPod by holding down the MENU and center buttons at the same time for 5 seconds. If it works, you should see an Apple logo, and it will work again. (3) If that doesn’t work, connect the iPod to your computer. When it shows up in iTunes, you will have to press “Restore iPod”. This will erase all songs, photos, videos, etc. from your iPod, but it fixes most problems like this.
You need a FireWire cable and power adapter to charge it. Cable: https://www.ebay.com/sch/i.html?_from=R4... Power adapter: https://www.ebay.com/sch/i.html?_from=R4... Note: Some eBay listings already include both things in them, since they are used together.
Just to be sure it isn’t a software problem, restore the iPod in iTunes first. If that doesn’t work, try replacing the display. And if that doesn’t work, you will need to replace the logic board. iPod 第4世代またはPhotoのディスプレイの交換 iPod 第4世代またはPhotoのロジックボードの交換
You need to replace the battery. It is VERY DIFFICULT to replace the battery in this iPod, but here’s a link to the logic board assembly repair guide. You will need to follow this guide, then replace the battery using a soldering iron. iPod Nano 6th Generation Logic Board Assembly Replacement
Have you tried restoring you iPod in iTunes? (1) Connect your iPod to a computer using the charging cable. (2) Open iTunes. iTunes usually opens automatically, but if it doesn’t, open it yourself. (3) Select the iPod in iTunes and click “Restore”. This will erase everything on your iPod. (4) After it is done restoring, you can put your music back onto the iPod.