The symmetry of the superconducting condensate in Sr2RuO4 remains controversial after recent experiments overturned the dominant chiral p-wave paradigm. We perform a theoretical study of pairing by spin- and chargefluctuations in Sr2RuO4, including the effects of spin-orbit coupling, and both local and longer-range Coulomb repulsion. The latter has important consequences for Sr2RuO4 due to the near-degeneracy of symmetry-distinct pairing states in this material. We find leading nodal s', d(xy), and helical (p) solutions, while both the g- and d(x2-y2)-wave channels remain noncompetitive. This suggests nodal time-reversal symmetry broken s'+ id(xy) or s,+ ip phases, promoted by longer-range Coulomb repulsion, as the most favorable candidates for Sr2RuO4. We analyze the properties of these states and show that the s'+ id(xy) solution agrees with the bulk of available experimental data.