Doug, mine was like yours. The P.O. had disconnected the heater hoses. Turned out my core was fine, it was the control valve that was bad and leaking.
I tested my heater core using a section cut out of a bicycle tube. Leaving the valve stem in and clamping the tube around the core pipes. Then submerged it in a tub of water and added air pressure to the tube.
No bubbles from the core, but the valve was leaking bad.
I'll back that up what 'Old GMC Gold' said, plus I tested mine hooked up to the hot engine with core on the fender. Didn't leak, but 3 miles down the road the valve diaphragm let loose. Replace the diaphragm even if it doesn't leak. The old rubber hardens with time then cracks, a matter of not if, but when. $10.00 at NAPA for the part.
