Hi Roger - Sorry I missed your post in the "Introductions" forum, so let me wish you a warm welcome in this thread
1. I assume you are talking about conversion to Nikon's DNG file format, not the Democratic National Committee (ie, DNC), file format, LOL. So, I am going to edit the title of this thread accordingly.
2. You do realize that your D600 came out many years after CS3 was released, don't you? This is an eternity in the software world. There is no way the developers of CS3 could have anticipated all the new features of the d600 that would eventually be incorporated into the d600's raw data files (i.e., NEF files) years after CS3 was released, and even after support for CS3 had stopped. This means that there is absolutely no way CS3 can read a d600's NEF file.
3. In your post you make no mention of Adobe's RAW to DNG converter software, so let me describe what it is, because you will need it.
To accommodate situations like yours (i.e., a modern camera and very, very old software), much to Adobe's credit, they have released a series of free file converters which change NEF (Nikon proprietary raw data files) to DNG (open source raw data files). They even have released some updates for old ACR software to allow some old versions of Photoshop to read DNG files. Please read the overview of the process here:
Next, select and download the appropriate version of the NEF-to-DNG converter from this page:
Install it, and use it to translate your d600's NEF files into DNG files.
If the ACR converter that came with CS3 is pre-DNG, then update the CS3 version of ACR to a version from the download page that will allow CS3 to read DNG files. It is your responsibility to select the correct versions of these files for your particular installation.
4. One last point: If I understand your last post, you seem to express a wish to have d600 NEF files automatically opened by CS3. Unfortunately, that just isn't going to happen. You have to go through the manual steps that are described in the first reference that I cited. I believe that at least some of the DNG converters allow one to batch convert a group of NEFs into a group of DNGs. Then, some of the ACR updates may allow you to open a set of DNGs, but, to be honest, this is such a tedious process, I have never actually done this myself. My recommendation is that if you want things to happen automatically, you should subscribe to the "photographer's" version of Adobe's Creative Cloud offering. I think it's about $20 USD per month. In addition to doing all of the above seamlessly and automatically, it allows you to access all of the improvements in this software in the last ten or so years since CS3 was discontinued. Of special interest to you might be the big improvements in the noise reduction software included in the last several years of ACR.