Apple Pencil 1st generation

Given your additional description, it is even more likely that you have acquired a Pencil with a “dead” battery.

Return to point of purchase for a refund - and then buy replacement from Apple. Apple will provide a 12 month warranty; if the battery fails, it’ll be replaced.

As described, you Apple Pencil battery is failing or has failed. Do you regularly use and recharge the pencil? Infrequently used Pencils often fail.

The tiny internal battery must never be allowed to remain in a discharged state for any period of time, as the battery will suffer irreparable damage. Once the battery has failed, as it cannot be serviced or replaced, the Pencil must be replaced.

Sorry, not the news you were hoping for.

Delighted to help. I hope your return, refund (and eventual replacement) happens without any issues.