TNG's problem, as mentioned above, is that the effects were edited in on video tape.. but at one point these would have had to be composited on film, and maybe that film is still available.. who knows? Heck, if the TOS prints are still around, there's gotta be TNG prints somewhere.
There are TNG original camera negatives as Okuda mentioned.
They were composited on videotape
at 480i resolution, not film.
Malcolm Orr mentions
they were able to find the exact scene they wanted from Menage a Trois for [re]scanning [the film to HD] for the finale of Enterprise, so presumably they are indexed in some way...
see this post
as to why if TNG were given a remastered treatment for Blu-ray why all of the visual effects would probably be done as CGI.
This episode "Parallels" had to do some major compositing. Check this out
about the difficulty in reconforming that episode from the original camera negative for the visual effects shot for a 5 seconds shot.