The battery is not replaceable. Attempting to do so will completely destroy your Apple Pencil.
The only possibility of reviving an apparently dead [first generation] Pencil is to connect it to your iPad for an extended period (not easy if you intend to use your iPad - as having the Pencil attached can risk physical damage, if jolted, to the Lightning port; safer to try this when you don’t intend to use your iPad for a couple of hours).
It’s perhaps worth noting that the Pencil, inexplicably, accepts charge faster when connected directly to the iPad - in preference to using the in-line adapter that permits connection to the iPad charging cable.
If you are lucky, your Pencil may (I stress - may) be revived. If you’re unlucky, and you’re outside of your Pencil warranty, then the only resolution is to purchase either a replacement - or an alternative compatible stylus.
Best of luck. I hope this helps.