  We generalize the multiband typical medium dynamical cluster approximation
and the formalism introduced by Blackman, Esterling and Berk so that it can
deal with localization in multiband disordered systems with both diagonal and
off-diagonal disorder with complicated potentials. We also introduce a new
ansatz for the angle resolved typical density of states that greatly improves
the numerical stability of the method while preserving the independence of
scattering events at different frequencies. Starting from the first-principles
effective Hamiltonian, we apply this method to the diluted magnetic
semiconductor Ga$_{1-x}$Mn$_x$N, and find the impurity band is completely
localized for Mn concentrations $x<0.03$ while for $0.03 <x<0.10$ the impurity
band has delocalized states but the chemical potential resides at or above the
mobility edge. So, the system is always insulating within the experimental
compositional limit ($x\approx 0.10$) due to Anderson localization. However,
for $0.03 <x<0.10$ hole doping could make the system metallic allowing double
exchange mediated, or enhanced, ferromagnetism. The developed method is
expected to have a large impact on first-principles studies of Anderson
localization.
