How do I break the DFU mode cycle on an old iPod touch (2nd gen)?

My daughter was gifted an ipod touch (2nd gen circa 2008). I have tried to restart this thing twenty times or more but it still comes up with the same course of action being required.

The only thing the screen of the device will show is the image attached. When the device is plugged into itunes a message about DFU appears. But I can't seem to break the cycle the device is stuck in. Itunes only offers the message: This ipod was previously in DFU mode, but restarted and is no longer in DFU mode. To restore this ipod from DFU mode, disconnect it and place it into DFU mode. Thing is, it won't allow me to put it into DFU mode. Anyone dealt with this before? I've searched the web for answers but have not found anything that will get me to DFU.

[Re-Titled by Moderator]