If a new order is issued in a custody modification, does the other party still have to pay the money written into the original

It sounds as if the first order dealt with contempt and resulted in a judgment. That is due unless paid or specifically dealt with in a later action. A modification is prospective only and has nothing to do with judgments that have already occurred. The original judgment is still in affect as long as it has not been paid, subject to any existing statute of limitations.