the cable is going to be the easy find because the knob will be too eay to turn.
as for a blown heater core you would most likely smell coolant in the car or start getting a film on the inside of your windows, not really all that likely.
as far the plugged core, i find them at work but pulling the heater hoses off both ends (inlet and outlet) and forcing water through the heater core with a garden hose, if it dribbles out or takes a lot of force to try and get some out it's most likely a heater core, they make some flush stuff available to try and clean it out but ive never used it.
as for a broken blend door, get under the dash (right side) and follow the cable till you see where it attaches and that should be the blend door, try moving it by hand (with the cable disconnected) and if it feels too easy or you hear something rattling around you may have a broken blend door.
as for the coolant level, thats obvious,
as for the air, it should work its way out. it shouldnt be there in the first place so unless you had done some recent work where you needed to be around the coolant i would imagine you have a leak somewhere
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most of these precedures can be a little more complex than i got into so if you have questions let me know.
hope it helps someone
