i have a nexus 5 D820 which has the same problem. On closer inspection of motherboard i found that one coil is damaged which causes the back light problem. then i just push it after that the phone was working perfectly for some time.
unfortunately i cannot permanently fix this coil..now i need to replace it..
can any body tell me the name of this part.... see the picture in the link and
http://i59.tinypic.com/o6yxw7.jpg