If yours is not a factory AC car, it is fairly easy to remove the heater box in your Dart. First remove the glovebox inside shell. Be careful since that is cardboard (replacements available). As I recall, the wiring and cables are so simple you don't even need to label them (no vacuum hoses if non-AC). Once you pull the box, everything will appear simple and obvious, and a great chance to clean out the dead rodents and candy bars that give that "old car aroma". I am basing that on my 65 non-AC box. My 69 Dart's was complicated, but that was factory AC. One trick is the nuts at the bottom of the long rods that run up the fresh air vents to hook the cowl at the top. Use WD-40 once you find them.
I like 65-440's explanation of his blocked water flow experience. At first, I braced myself for another strange "too high water velocity" type theories people throw out that conflicts with Physics, but it make sense that the water might not be flowing but the hoses could still get hot on both sides from natural convection within the hose on each side. Of course, testing the heater core alone with a garden hose could easily determine if plugged, but be careful since home water runs 60 psi and can break a perfectly good heater core. New ones for a Dart are pretty cheap ($30 for mine), much better than my Mercedes 300D (~$400).