Fisherman,
There are no valves in the TMI cooling system that when closed prevent coolant flow.
The valve in question failed in the open position after it relieved a pressure spike. The continued outflow from that valve dropped the pressure in the TMI primary system. As the pressure went down, so did the boiling point of the water. It got to a point at which the temperature in the core which is not high enough to boil the water at nominal pressure was able to boil the coolant at the reduced pressure. The core was being cooled by a two-phase mixture of steam and water.
However, the core was undamaged at that point, and the TMI accident was totally reversible up to 90 minutes into the accident. It was at that time that the operators, who were unaware of the fact that the coolant was boiling because they never checked their steam tables, decided that the primary coolant pumps should be stopped because they were making strange noises.
Those strange noises were a badly needed clue that the operators ignored. The reason the pumps were complaining is because they were pumping a two-phase steam and water mixture. The operators missed that.
They decided to "save" the pumps, and in so doing "lost" the reactor.
Dr. Gregory Greenman