While the valve is a likely cause of the non-flow, if you have a heater core that has not been flowing for a looong time, it is also possible the heater core is plugged up. The passages inside are small and over time old coolant gels and hardens. I would disconnect the heater hoses at the motor and loosely (so you don't build up too much pressure) use a garden hose and see if you can get any flow through the heater hoses and heater core. Once you know you have good flow you can work on the valve. Very common for the valves to leak and get stuck.