What I do on no power apple devices with lightning connectors is either charge the battery externally or plug in an adapter that allows powering the phone off a DC bench power supply.
If the phone ends up turning on I can pretty much safely say the charging chip needs to be replaced. Anything board level on iPods IMO is not going to be worth fixing.
The battery is soldered on so what I would do is externally charge the lithium battery with 4.7V from a DC bench power supply and then re-solder back on and see if it turns on.
It’s most likely either going to be a bad battery or charging chip gone bad (can’t charge flat batteries).
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