2002 Dodge Intrepid water draining from evaporator vent tub

Engine Cooling problem
2002 Dodge Intrepid 4 cyl Front Wheel Drive Automatic 100k miles

I have to constantly add water to my car. After crawling underneath it, I found water draining from my evaporator vent line. I know this is normal (condensation) when the A/C is running, but it is just short of pouring out and the A/C is not running. Also there is air blowing from the tube (even when the heater/AC fan motor is not on) - not sure if this is normal. Anyways, I am leaning towards thinking the heater core is leaking, but wanted to ask around before diving into that project.