At 3 decades old there could have been any number of changes made to this system over the years by who knows how many owners.
Can you clarify what "pump tests OK" means? To me, that would mean that you disconnected the output hose, turned on the pump and had good water flow/pressure coming out.
If you add more information and clarify better, that will help us. Meaning, normally if someone says a faucet doesn't work then we look for a bad motor, filter blockage or line blockage/leak.