As described, your Apple Pencil may be displaying symptoms of a dead battery - that will not accept or hold any charge.
First, ensure that you have updated your iPad to iPadOS 13.6. This update addresses a number of issues with some models of iPad, most notably iPad Air3, that relate to pairing and operation of Apple Pencil. Whilst you have a different iPad, the update is good place to start.
Assuming that you do not have any other iPad charging issues - and that the Lightning Port of your iPad is free from debris - whilst the Pencil is plugged-in to the Lightning Port of your iPad, verify that the Pencil is recognised:
Settings > General > About
Scroll to the bottom of the page - and you should find two identical entries for the Pencil (one each for the physical and Bluetooth connections). Two entries illustrates that both the Lightning and BTLE radio interfaces are good. If either are missing, then the Pencil is very likely defective.
The tiny internal Li-ion battery is susceptible to permanent/irreversible damage through being left discharged for long periods. Even some “new” pencils can exhibit signs of failure out-of-the-box if they are “old stock”.
It is essential that if you have an Apple Pencil that you charge it regularly - whether used or not - so as to protect the battery from deep-discharge. Do not allow a pencil to remain in low-charge state for any period of time - as the internal battery will fail, rendering the Pencil useless.
If the Pencil Battery has failed, the only remedy is to replace the Pencil. If purchased directly from Apple, should the battery have failed whilst your pencil is within its one-year warranty, you should look to having it replaced at an Apple Store.
Here is one of the better troubleshooting guides for the Apple Pencil - which may also prove to be helpful:
https://appletoolbox.com/apple-pencil-not-working-heres-our-troubleshooting-guide/
I hope this information proves to be helpful in both diagnosing and resolving the problem. Do let us know how you get on.
