iPad (5th gen) stuck in DFU mode and won't restore through iTunes

Yesterday, my 2 year-old 5th generation iPad just died in the middle of watching a show on an app. It had been charged, has never been dropped, not near water, the cables work fine. No problems til now. iOS 14, but hadn't installed the latest couple of updates. It wouldn't let me do a hard reset. It was just a blank, black screen.

Tried to restore through iTunes, and it couldn't complete the process due to an unknown error. Presumably because the iPad is in DFU mode and not recovery mode. I can't get it out of DFU mode, even using a downloaded toolkit (Dr. Fone).

Now it occasionally goes to a dark navy screen for no apparent reason (ghostly possession?), but it will not show the apple logo when pressing power and home no matter how much I plead with it.

I'm at my wit's end. If we weren't in a pandemic, I'd consider going to a Genius bar. But all things considered, I'd really rather not.

Any and all suggestions welcome.