  We propose a M(atrix) model for N=4 $SU(k)$ Super-Yang-Mills theory
compactified on $T^4$. In this model it is possible to make $T^4$
noncommutative and it is easy to turn on all 6 components of the
noncommutativity on $T^4$. The action of S-duality on the noncommutativity
parameters is also manifest. The M(atrix)-model is given by the large $N$ limit
of a $\sigma$-model on $T^2$ whose target space is the moduli space of $k$
SU(N) instantons on $T^3\times R$. We also propose that the $SU(k)$ 2+1D
$Spin(8)$ theory (the low-energy description of $k$ M2-branes) on $T^3$
corresponds to the large $N$ limit of an integral over the latter instanton
moduli space. The identification is based on the fact that Euclidean wrapped
M2-branes in toroidally compactified M-theory correspond to instantons in the
M(atrix)-model. In the new M(atrix) models, operators with nonzero momentum
along $T^3$ (or $T^4$) correspond to insertions of Wilson lines along a 1-cycle
that is determined by the momentum. Momentum is conserved in the large $N$
limit.
