We present studies of the electronic structure of La₂₋xBaxCuO₄, a system where the superconductivity is strongly suppressed as static spin and charge orders or "stripes" develop near the doping level of x = fraction one-eighth. Using angle-resolved photoemission and scanning tunneling microscopy, we detect an energy gap at the Fermi surface with magnitude consistent with d-wave symmetry and with linear density of states, vanishing only at four nodal points, even when superconductivity disappears at x = fraction one-eighth. Thus, the nonsuperconducting, striped state at x = fraction one-eighth is consistent with a phase-incoherent d-wave superconductor whose Cooper pairs form spin-charge-ordered structures instead of becoming superconducting.