A quick check for the Raduino is to pull it from the main board, connect a miniUSB cable to the Nano (socket is between the Nano board and the Raduino board) and supply a standard 5v USB power to the USB cord. If the display lights, and the operation of the Raduino seems normal, then the problem is on the main board.
If the Raduino display will not light, then it is possible that the problem is the 5vdc regulator failed on overvoltage. Only what that I know would be to remove from the board and try USB power again.
What test equipment do you have access to? Since you reported voltage and continuity measurements I would assume at least a multi meter or DVM.