Final answer:
The nurse should administer the TPN solution via gravity drip while waiting for a new infusion pump to maintain the proper administration rate and prevent any complications.
Step-by-step explanation:
In a situation where a nurse discovers that the infusion pump used for administering total parenteral nutrition (TPN) has stopped working, the correct action while waiting for a new infusion pump would be to administer the TPN solution via a gravity drip. This is because TPN solutions are specialized and often hypertonic, which requires strict regulation of their administration rate to prevent complications like hyperglycemia or fluid overload. Therefore, the nurse should not increase the rate of TPN infusion manually, switch to oral nutrition supplements, or discontinue the infusion entirely unless specifically indicated by the patient's care protocol.