Here is one of the better troubleshooting guides for the Apple Pencil - that may be helpful in working through common issues.
https://appletoolbox.com/apple-pencil-not-working-heres-our-troubleshooting-guide/
Your Apple Pencil is exhibiting symptoms of a dead battery - that will not accept or hold any charge.
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. Setting aside an unused Pencil, for extended periods, is a recipe for premature death of the Pencil battery.
If the Pencil Battery has failed, the only remedy is to replace the Pencil. If the battery has failed and your pencil is within its one-year warranty, you should look to having it replaced by your retailer or at an Apple Store.
Some reports suggest that gentle warming of the Pencil (such as a hot water radiator) prior to attempting charging of the Pencil can resurrect a Pencil battery. Whilst nobody should advocate external heating of any Li-ion battery, gentle external heating of the tiny Pencil battery is unlikely to cause concern.
I hope this information proves to be helpful in both diagnosing and resolving the problem.
