The heater is working, if you touch the duct is hot. but no air is blowing out.

If flow and return hoses are hot, then heater is hot..and problem is with ducting valves.. Missing or jammed

could be broken ducting letting hot air escape or on the intake side drawing too much outside air in. could be the fan unit not pushing enough air

could be blend doors in heating duct work.

I like that you were knowledgeable to check both coolant lines tells me you are getting hot coolant through the heater core next thing to check will be the blend door on the inside of your vehicle. The blend door is a door that switches from cold air duct to heater duct depending on what you are using at the time. If it is stuck on the cold air duct you will not get any heat sometimes these doors are vacuum actuated and sometimes they are electrically actuated most the time you are able to see the movement of the motor from inside if you don't see any movement but you hear it move chances are it is the door blend I hope this helps.

Always make sure you set it to the right position. e.g, winter period turn it to the red side while in summer you turn it to the green side.

It does blow correct? Just not hot air? This shop replaced the control head (the unit that the knobs are connected to)? I'm assuming the answer to all is yes. There may be a jam. Not too common but I've seen it a couple times. There are doors within the air box under your dash where your blower motor and heater core are. The control head controls these doors, opening one vent door to outside air and/or to the evaporator, closing the other vent door to the heater core or vise versa. It also controls the doors which direct air to certain ducts that will blow out the selected vents. If something has been droped down through a vent and worked its way to these doors I'm talking about, it could jam the door closed that goes to the heater core, preventing heat from blowing through the ducts.

The heater operates from the hot water from the engine cooling system flowing through the heater radiator which is inside the air ducts under the dash. I suspect that the control wire/cable that goes from the heater control lever has broken or become disconnected from the heater tap that controls the volume of hot water through the heater radiator. Some times there is also a flap in the air ducts that is operated by the heater lever tha varies the amount of air that is heated. The tap may be in the engine bay or tucked in behind the air ducting.

Either a faulty thermostat or air in the system. Bleed the system and you still have no heater then get a new thermostat put in.

It seems to me if your heater core is hot, and the fan blows cold air, then your ducting is closed off. Try and see if your duct door is opening up. You say you changed out your controls, but it sounds as though it wasn't your controls that were bad, but what they control is not opening up.
It's all well and good that the heater core is getting hot, but if the fan cannot deliver that hot air passing through it, then walah.
It has to be an air duct obstruction. Either the ducting is collapsed, the duct door is not opening, or you have some obstruction blocking the ducting. My guess, because that is all I can give you without seeing for myself, is that the linkeage or solonoid that opens the duct door is not working. Older cars had a cable, but I believe newer use a solonoid to operate the opening and closing of the door. The door is there so you don't get the heat from the core when you are using AC.
Hope this helps.

if you claim that your heater core is flushed properly then my bet is the temp regulator is bad.