Then I noticed this plastic piece in between the battery and the contact on the battery holder.

My guess is that it was inserted by factory that makes the logic boards and was supposed to be removed during final assembly of the machine, but this one got missed and has been there for 15+ years.
I measured the battery and it was reading 3.4volts still, so I put it back in, sans plastic piece, and it’s working fine now.

My guess is that it was inserted by factory that makes the logic boards and was supposed to be removed during final assembly of the machine, but this one got missed and has been there for 15+ years.
I measured the battery and it was reading 3.4volts still, so I put it back in, sans plastic piece, and it’s working fine now.