How get a genius appointment when I don't know the serial number of my iPad?

There are many ways to obtain that serial number. Even if the iPad does not power on, the serial number is on the back of the device.

Here are details.

Find the serial number or IMEI on your iPhone, iPad, or iPod touch - Apple Support

Hi Oldie63!

In my opinion, the easiest way to find out your serial number, is by following these steps:

[Settings > General > About], then you can see your serial number, copy it, and schedule your Genius Bar Appointment.

If you have the Apple Support app and it is signed in to the same Apple ID as your iPad, follow these steps:

[Apple Support App > Choose your device > Device Details > Serial Number].

This document can relay the message in different words: Find the serial number or IMEI on your iPhone, iPad, or iPod touch - Apple Support

Take Care and Good Luck!

To find your iPad serial number, simply sign-in to your AppleID account from any computer using a web-browser:

https://appleid.apple.com

Having signed-in, open the Devices tab. Here you will find an entry for every device associated with your AppleID; tap the related entry to see full technical details of the device - including Serial Numbers and IMEI/MEID of Cellular devices.