Coolant needs to flow freely in the system. An air pocket acts like a physical wall to the liquid coolant -- the coolant hits the wall and just stops flowing. An air pocket near the heater core can stop the hot coolant from flowing through the heater core. If the coolant lines in the heater core do not get hot (no hot coolant in core lines, only cold coolant) the heat exchanger has no heat to warm the air crossing over the heat exchanger in the core. Clogged heater core coolant lines also create the same situation in the heater core.
What vintagespin said for bleeding works well. I will add to that to occasionally squeeze with your hand the upper radiator hose while following his steps -- this will help force coolant past any air pockets in the system and move the air pocket to the bleeder valve. Also, raising the coolant reservoir at times with your hands so it is higher by 6 inches or so than it normally sits, while tilting it slightly so the bigger hose in front points more to the ground, will help move coolant into the system. The engine must get the coolant hot to properly bleed the system. Here is another way to bleed the system......clickyclick
. Also know, that multiple cycles of the above bleeding methods, letting the coolant cool and get hot , may have to be done to properly remove any air pockets from the system.
Tips.....put a rag or something around the bleeder valve to catch the hot coolant that comes out of it. Also, if you have not filled the coolant system up yet, I would just run straight distilled water in the system until you can get the heater working as you want it. Once get the heater working properly, drain the water from the system at the lower radiator hose and refill and re-bleed with 50/50 mix of coolant. You will not be able to drain all the distilled water from the system, but adding in a 50/50 mix will still keep you within a final 60/40 water/coolant mix which is fine. Using straight distilled water for now will be easier/cheaper than using new coolant again if you go after the heater core later. Also, the use of straight water then draining it will further flush the system for you. But, don't leave your system filled with water overnight! It will freeze and crack your block!
I've re-read this thread. I'm trying to understand where you are at right now. I read that you have drained the coolant from the car, back flushed the heater core, and refilled the coolant system. Is that right? If that is where you are at, I'd re-bleed the system as we've suggested to eliminate the possibility of any air pockets in the system before going after the heater core. If you feel confident you've done the bleeding right, and you want to replace the heater core, drain the system replace the core and the J-plug and o-ring (its cheap and easy insurance against future failure and you have the coolant drained out of the system).