1st generation pencil

This behaviour generally indicates a failed Pencil battery - for which the only remedy is replacement of the Pencil.

Here is Apple’s guide for pairing and using the Apple Pencil:

Connect Apple Pencil with your iPad - Apple Support

If still having difficulties, 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/

If you have checked through potential issues using the linked troubleshooting guide, then your Apple Pencil may be displaying symptoms of a dead battery - that will not accept or hold any charge.

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 entries for the Pencil (iPadOS13 and earlier: one each for the physical and Bluetooth connections. iPadOS14: sometimes only one entry). Finding these listed entries suggests that the Pencil electronics are good - otherwise, you have a totally dead pencil.

Check the Battery Widget for the charge status of the Pencil. Is it 100%? If not, let the Pencil charge; if it is fully charged, disconnect from the iPad. 

When disconnected from iPad, does the Pencil disappear from the Battery Widget - or it’s indicated state of charge suddenly fall? If either of these are true, then the Pencil battery is likely to be failing or dead.

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.

I hope this information proves to be helpful in both diagnosing and resolving the problem.

You have broke the battery

You cannot store Apple Pencils for any prolonged period of time and NOT keep them charged up to some level.

If your Apple Pencil/s sat around unused or unopened and not kept charged up for more than a few weeks, or so, OR

LONGER, then the battery in your Apple Pencil may have failed and is dead and you will have to purchase another

brand new Apple Pencil or get, if still under warranty, a free replacement Pencil from Apple.

Sorry.

And it looks like some things about the Apple Pencil have NOT changed in the new version 2 model, either.

FYI and something Apple will never, EVER divulge to it potential iPad Pro/Apple Pencil customers/users unless the potential customer/user is smart enough to ask about,

Due to the “always on and active/standby” nature of the Apple Pencil and, also, due to its very tiny rechargeable Li-

ion battery ( smaller than the eraser head on a REAL wooden pencil ), the Apple Pencil needs to be constantly charged up to some significant charge level ALL THE TIME, even when not using the Pencil for prolonged periods of time.

The Apple Pencil needs to be kept charged to a minimum of 5-10% all the time.

If the Apple Pencil battery is allowed to drain down to 0% and allowed to stay in that flat condition for more than a few weeks, or so, OR EVEN LONGER, that very tiny little Li-ion battery is too small to keep at a 0% state for a long period of time and it will fail and the Apple Pencil will be dead and you may have to “pop” for another $99 Apple Pencil, once again!

Apple only has a one-year warranty on any Apple accessory items.

You need to keep your Apple Pencil charged all the time, even if it is only to 10%-15% charge. It must keep some charge level in that tiny Lithium-ion battery at all times!

One last ditch thing you can try is to plug the Pencil's Lightning connector into the iPad.

Then, try a simple hard reset of your iPad by holding down both the Home and sleep/wake buttons simultaneously until your iPad goes to black and restarts with Apple logo, then release the buttons.

See if the Pencil starts charging then, when it reaches a sufficient charge, like over 15%, or so, or more, disconnect the Pencil and reconnect it to see if it Bluetooth pairs.

If it does pair, try using it.

Someone else posted another possible idea/solution that you can try before completely giving up on your Apple Pencil.

Try heating up your Pencil using a hair dryer on its highest setting for 5-10 minutes.

Do not get the hair dryer heat too close to the Pencil.

Or try leaving it near a heating register where you live for 10-15 minutes, or so.

See if this will revive the battery, or not.

If still no joy, your Pencil is definitely dead.

Sorry and Best of Luck to You!