Apple Pencil 2 won't connect with my iPad

First - verify compatibility. Here is the full list - ensure that you have an iPad that is compatible with the Apple Pencil - and the Pencil that you have:

Apple Pencil (2nd generation)

You can use Apple Pencil (2nd generation) with these iPad models: 

• iPad Air (4th generation)
• iPad Pro 12.9-inch (3rd generation) and later
• iPad Pro 11-inch (1st generation) and later

Apple Pencil (1st generation)

You can use Apple Pencil (1st generation) with these iPad models:

• iPad (8th generation)
• iPad mini (5th generation)
• iPad (7th generation)
• iPad (6th generation)
• iPad Air (3rd generation)
• iPad Pro 12.9-inch (1st or 2nd generation)
• iPad Pro 10.5-inch
• iPad Pro 9.7-inch

Not sure which iPad you have? Identify your iPad model.

The first and second generation Pencil use an entirely different pairing and charging interface. The second generation Pencil can only be used with iPad models that have the magnetic/inductive dock that is exclusively designed for the Pencil. Charging is controlled via the iPad magnetic dock

Here is one of the better troubleshooting guides for the Apple Pencil that may be helpful in working through common issues. This is applicable to all models of iPad and Apple Pencil:

https://appletoolbox.com/apple-pencil-not-working-heres-our-troubleshooting-guide/

If your Pencil is compatible with your iPad, and 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 two identical entries for the Pencil (one each for the physical and Bluetooth connections). Finding both entries suggests that the Pencil electronics are good.

Check the Battery Widget for the charge status of the Pencil. Is it 100%? if not, let it 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 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.

If the Pencil Battery has failed, the only remedy is to replace the Pencil. If purchased directly from Apple, if the battery has failed and your pencil is within its one-year warranty, you should look to having it replaced at an Apple Store.

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