Need to backup iPod, cannot unlock.

I have a ipod touch 5th generation. The touchscreen does not respond to touch. I need to get a backup of the device. When I connect to itunes, it says I need to unlock the device by entering the PIN on the device. I cannot do this because the ipod is not touch responsive.

Apple says they do not do data retrieval.

Is there anything I can do to get a backup of this device short of ordering a new screen?