You have (or had) 4168 images on the C drive in the Pictures folder. Are you saying that you did not move those to the NAS? Then are those still there?
Is this the catalog that you started with -- un-changed -- from before you moved the files? Or did you do something trying to recreate? You should NOT have done anything to create a new catalog, to import any photos, synchronize any folders or photos. All those things will just make a mess.
THe basic process is EITHER:
1) Exit lightroom
2) Move one or more folders that were in the lightroom catalog to another location
3) Start lightroom in the same catalog.
4) Use the option to point those folders, in lightroom, to their new locaiton.
OR DO THIS INSTEAD:
1) With lightroom running.
2) Get access to the new drive space (e.g. create a top level folder on the new drive in lightroom).
3) Drag and drop the folders from their old location in lightroom (NOT in explorer) to the new folder in lightroom.
In the first case you are moving things outside of lightroom, in the second case you let lightroom do the move (and it will update the catalog).
If you did not do one of these, I think for someone to help you more, we need a pretty detailed list of the steps you did take.