Can I transfer data from my old iPad to my new iPad even though my old iPad is dead and will not charge?

If your “old” iPad will not power-on, you cannot recover any data stored on the device. However, if you have either an iCloud or iTunes backup of the device, prior to its demise, you can restore the backup directly to your new iPad:

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Be aware that you cannot selectively restore from the backup - its all or nothing - and the restored backup will replace any data on the target device to which the backup is restored.