Q: iPod classic doesn't hold charge

I just purchased Universal Media Interface for my old Mercedes C300, and it came with iPod Classic.

It's okay while plugged to the car / wall usb, but it doesn't hold charge (it shut down immediately after unplug), and it cannot charge (power won't turn on, screen blinking) when plug to computer / macbook.

I thought I should replace battery. But can I resolve this issue another way?