Updating to iOS 8.4 has locked up my iPad2!

After upgrading early Wednesday morning to iOS 8.4 on my iPhone 6 and iPad2, I've now got a working phone but a non-working iPad2. When I power the iPad on, the Apple icon appears briefly, followed by a graphic urging me to connect to iTunes with a USB cable. But iTunes won't recognize my iPad, and the screen remains stuck on that graphic. I've tried forced restarts and putting it into recovery mode, but it always comes back to this connect-to-iTunes graphic. Is my iPad fried, or what?