2002 Mitsubishi Galant, No cabin Heat for 2 years!

I'm hoping someone can help me. My heat used to work until one day two years ago, I heard a strange clicking noise from my dash as I switched the climate control from cold to hot. After that incident, I have had no heat. I took it to a mechanic, only to be told that I antifreeze. Filled the radiator with antifreeze, heat never came back. Then I was told we need a new heater core, purchased a new heater core, heat lasted for a day or so, then no heat. I flushed the radiator, and still, the heat has not returned. We proceeded to change vital engine parts: T-stat, Water pump, oil pump, serpentine/timing belts, and the radiator itself. Now the heat only "halfway works". The heat only works when the setting is on zero (0), and only after 30+ minutes of driving. I have to let the heat build up without the fan blowing it, then I turn it on three(3) to get 10 seconds of full powered heat. After 10 seconds, it cools down, and eventually goes completely cold, whereas I have to turn it back to zero (0), and drive some more and repeat the process. It's very irritating. I have seen many many MANY people with the same problem all over the internet and no one has a solution. Even Mitsubishi couldn't help me. Please, if anyone has any insight, please give me a solution. Thanks in advance. I will donate if someone gives me a working solution.