iPod Classic only works when plugged in

I bought a used, refurbished 160GB 7th Gen iPod Classic last year. One day it suddenly started crashing constantly and now will crash instantly if it’s not charging. Even after hours of charging, the iPod will almost immediately say it is out of battery when it is unplugged and will endlessly reboot itself after that. It works perfectly when plugged in though. Even when the screen shows the battery icon at full charge when plugged in, it still says it is out of battery immediately after being unplugged. Sometimes I can listen to audio for about 30 minutes unplugged if I start listening before unplugging it, but it will then freeze up on it’s own. If I navigate any playlists before then, it says it’s out of battery and crashes. Sometimes after crashing repeatedly it will tell me to restore the iPod or will put itself into disk mode. If I try to reboot it manually, it crashes. Even after all of this, the moment I plug it in again, it works fine.

I’ve accessed diagnostics mode after unplugging it, and the battery levels are always maxed out. The hard drive shows 0 Reallocs, 0 Pending Sectors, but almost 100’000 Start/Stops (if that’s important).

I’ve restored the iPod twice. I’ve tried removing almost all the storage on it and removing almost all the playlists. It’s still behaving the same way.

When looking at other forum posts online, the two main suggestions are that either the battery is not connected properly or the logic board is faulty. I’d really appreciate feedback about which of these to replace.

Thanks in advance!