Hello ncauthron,
Thank you for posting to Apple Support Communities.
We understand you're having trouble restoring an iPad using iTunes. If you're using a Windows PC, make sure that iTunes is up-to-date: Update to the latest version of iTunes for Windows 10 - Apple Support If you're using a Mac, make sure your Mac is up-to-date: Update macOS on Mac - Apple Support
Updated software can resolve some incompatibility issues to recognizing your iPad when going through the restore process.
Additionally, Apple has a couple great articles that can help you with resolving issues related to restoring the iPad and it not being recognized. Take a look:
Restore your iPhone, iPad, or iPod to factory settings - Apple Support
If your computer doesn't recognize your iPhone or iPad - Apple Support
1. Look in the Finder or iTunes
On a Mac with macOS Catalina or later, look for your device in the sidebar of any window in the Finder.*
On a Mac with an earlier version of macOS, look for your device in iTunes.
On a PC with iTunes for Windows, look for your device in iTunes.
Learn more about viewing your device in the Finder or iTunes
2. Update the software on all devices
Update your iPhone or iPad
Update your Mac
Update your Windows PC
On your PC you might also need to update iTunes and update drivers.
3. Connect your device directly to your computer
Make sure that your device is unlocked and showing its Home Screen, then use a USB cable to connect it directly to your computer. Don't connect to a USB hub, display, or other device.
If that doesn't help, disconnect your device and all other USB devices and accessories from your computer. Then reconnect only your device.
4. Trust your computer, if asked
If you see a “Trust this Computer?” alert on your device when you plug it into your computer, tap Trust.
About the 'Trust This Computer' alert
5. Allow the accessory to connect
When connecting your device to a Mac laptop computer with Apple silicon, your Mac might ask whether you want to allow this accessory to connect. If so, allow it to connect.
Learn about allowing accessories to connect
6. Restart your devices
Restart your iPhone
Restart your iPad
Restart your Mac
Restart your Windows PC
7. Try a different port, cable, or computer
The issue could be related to your computer, its USB port, or the USB cable connecting it to your device. If possible, try a different computer, USB port, or USB cable. Also check for any debris in the charging port on the bottom of your iPhone or iPad.
8. Contact us
If your computer still doesn't recognize your iPhone or iPad, contact Apple Support.
If you're still having trouble after looking through those articles, we recommend contacting Apple Support: Contact Apple Support
Take care.