Error 21/2001 cannot be resolved

My phone was happily streaming radio and then turned itself off. It will not restart. I've tried all the usual suggestions for restoring the phone, as per Apple's help pages and various other sites - but sadly the restore process hangs with an error code 21 (Windows)/2001 (OSX).

I've tried different usb cables, different computers, different OS, replacing the battery with a new one, reconnecting the sensor ribbon. iTunes, and OS are all up to date too.

I'd really appreciate some other pointers on what to try next. Ideally I'd like some type of diagnostic software that might be available to at least get some meaningful debug data back.

Here's hoping......