Hi Vitoburrito,
welcome to this Apple (user-to-user) Community!
Re: "I need help with my iPod classic from 2005:
I tried to download music onto it from my computer but iTunes wouldn’t work"
Am no expert in this area, yet your post deserves some response.
On macOS Mojave or earlier or a Windows PC, you can use iTunes to sync music, movies, and more.
Use iTunes to sync your iPhone, iPad, or iPod with your computer - Apple Support
or
If you wish: Learn how to redownload apps and redownload music that you purchased on another device.
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Re:" ... maybe I could sync it and download music but it’s not working and I don’t know what to do"
Else: wondering if Apple support's online article (link below) can help guide you:
(Note: Please choose the correct MacOS version at the top of the article, for accurate info.}
Sync music between your Mac and iPhone, iPad, or iPod touch - Apple Support
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Re: "also a lot of YouTube videos aren’t working and I don’t want to go to a repair shop since it’s not worth it"
Am unsure what "not workng" means ...eg: videos not syncing ? ... videos on iPod won't play ?
If useful to you: You can: Identify your iPod model - Apple Support
and
Manuals, Specs, and Downloads - Apple Support may have the correct manual / user guide