  We classify those manifolds mentioned in the title which have finite
topological type. Namely we show any such connected M is isomorphic to a
hyperkaehler quotient of a flat quaternionic vector space by an abelian group.
  We also show that a compact connected and simply connected 3-Sasakian
manifold of dimension 4n-1 whose isometry group has rank n+1 is isometric to a
3-Sasakian quotient of a sphere by a torus. As a corollary, a compact connected
quaternion-Kaehler 4n-manifold with positive scalar curvature and isometry
group of rank n+1 is isometric to the quaternionic projective space or the
complex grassmanian.
