Usually resolved by replacing the LCD, well always out of my experience but I'm sure sometimes it could be Board Related. First thing I'd try would be a LCD change, this isn't sold on Ifixit yet so here's a link:
http://www.ebay.co.uk/itm/IPOD-NANO-7-7TH-GEN-7G-LCD-SCREEN-DISPLAY-REPLACEMENT-APPLE-/300884014148?pt=UK_Replacement_Parts_Tools&hash=item460e15b444#shId
From eBay UK but if you look I'm sure it will be on eBay.com as well.
Please read through this guide before ordering, it will show you how complex it is and it will be up to you to decide whether you can do it or not.
[guide|10826]