It's a Hardware failure. Usually a failure in the Hardware will require the Logic Board to be replaced. Apple does note that the error code 1 is a Hardware Failure. Like any other electronic manufacturer, they do not do component repair on the Logic Board or troubleshoot to isolate the exact component failure, they will only replace the entire Logic Board.
If they are offering you the option to purchase a new iPad Pro 12.9" for $799, I would take that deal. You would expect to pay close to that just to have the Logic Board replaced on your device.
As with any error when restoring a device, always try using a different USB cable first to rule that out.