Doesn't work unless plugged in.

Hi @monkeyman18935

Battery replacement will only be the cost of the battery ( + shipping) if you do it yourself.

Here's the ifixit Разборка Kobo Mini guide.

The battery can be seen in the image in Step.3.

Not sure if it is glued down or not (most probably is) so be careful if you have to prise it out, that you don't puncture it. Use a syringe and run a line of Isopropyl Alcohol 99%+ (available from electronic parts stores) down the edge of the battery to loosen the adhesive underneath it. Then prise it up a bit at a time applying more alcohol each time. Do not use liberally as you don't want to make things too wet.

Remember to disconnect the battery as soon as you can access it so as to avoid the possibility of any electrical problems from occurring whilst doing the replacement.

Search online for GN344658 3.7V LiPo battery to find suppliers that suit you best. Here's just one example to give you an idea of the cost of the battery (+ shipping).

If you do decide to do it yourself, please dispose of the original battery responsibly. The environment will thank you for doing this.