The D600 is supported. Your files are likely corrupted. If you used Nikon Transfer v 1.x to copy from the camera that will corrupt them, although this tool can undo that specific damage: http://owl.phy.queensu.ca/~phil/exiftool/fix_corrupted_nef.html
If you have not used Nikon Transfer 1 then some other hardware component or driver might be iffy. A way to check if it is your files or the D600 format in particular is to download sample D600 files from the internet and see if they work. If the downloaded ones are ok then it’s something with your particular camera-to-computer transfer that’s corrupting them. Samples can be found at the DPReview D600 RAW Comparison review section:
Here is a download link for an ISO 100 shot:
How did you transfer the raw files to your computer? You didn't use an older version of Nikon Transfer did you? The older version seems to corrupt the metadata in recent Nikon Cameras. See this thread for more info: Unable to open D600 NEF files...
Thanks both of you. Yes I used the old Nikon Transfer. When I used the transfer in ViewNX2, it went fine. Again, thank you