Turquoise when mined, depending on the location, have different
degree of density. Most of it is low density and it is stabilized by
epoxy or similar compounds. Only small percentage is dense enough to
be used in jewellery without treatment. Turquoise of this quality is
sold locally, and almost impossible to obtain.
In your case it may be cheaper to replace stone, than trying to fix
it. Lapidary specializing in turquoise can advise you on the most
economical course of action.
However, since you mentioned white veining, it is also possibility
that you may be dealing with synthetic turquoise.
Take a 10x loop and examine the stone. If you can see while grain in
the blue background, almost like cooked farina, it is synthetic.
Other possibility is that original matrix was bleached out before
dying stone blue.
That type of treatment goes far beyond regular stabilization and
stone cannot be very expensive.