  We investigate the ground-state phase diagram of the quarter-filled Hubbard
ladder with nearest-neighbor Coulomb repulsion V using the Density Matrix
Renormalization Group technique. The ground-state is homogeneous at small V, a
``checkerboard'' charge--ordered insulator at large V and not too small on-site
Coulomb repulsion U, and is phase-separated for moderate or large V and small
U. The zero-temperature transition between the homogeneous and the
charge-ordered phase is found to be second order. In both the homogeneous and
the charge-ordered phases the existence of a spin gap mainly depends on the
ratio of interchain to intrachain hopping. In the second part of the paper, we
construct an effective Hamiltonian for the spin degrees of freedom in the
strong-coupling charge-ordered regime which maps the system onto a frustrated
spin chain. The opening of a spin gap is thus connected with spontaneous
dimerization.
