You need LR 6.12/CC 2015.12 with ACR 9.12 for that camera. You can use the Free DNG converter, 9.12, to convert them to DNGs.
I see you think you have most current version of the DNG convert but open it and check that you are actually running the 9.12 version of the converter. Click the button at the bottom "About DNG Converter".
To use the DNG converter you have to Copy the NEF files to a folder on your drive. Then in the DNG converter point it to that folder. You can't, AFAIK, use the converter on the SD card and especially if you are connecting the camera directly to the computer.
The other problem could be if you used Nikon Transfer to download the images. That Nikon utility can make NEF files not readable by Adobe software. My experience has been that you should be able to use the DNG converter as the software to download the images from the SD card. I have done that many times, although I have always used a card reader. I have never downloaded directly from the camera.