Long drown out slog of a war with no real winners. Chile might have been able to hold their frontiers against Argentina, but they would have been worn down in a war of attrition. Bolivia was and is a non entity in terms of this scenario, their political system was weak, and their military could have been defeated by the Chilean police force let alone the Cabinero's. Peru, alone could be taken by Chile, but when they are allied with a militarily active Argentina then Chile loses. They go down hard, but Chile didn't have the manpower needed to win that sort of long slogging war. The only chance that the Chileans would have would be if the Argentine and Peruvian political processes broke down, which is a possibility, especially if Chile can win some decisive battles early in the war.
Brazil probably sits the war out and laughs, as this would leave them as the power on the continent and they didn't really have any investment in the conflict. Ecuador is a bit of a joker though, they had and have a long running dispute with Peru and if the Peruvians get bogged down enough they might have the moxie to try for a back stab, or at least threaten one enough that the Peruvians would be forced to buy them off diplomatically.