Ok, first of all, I am no expert, but I would like to remind you be aware of whoever is working on your car, since they replaced totally unrelated parts. Since you still have heat in the back, that clearly indicates it's not the thermostat. The only reason to replace it is when your engine is running on low temperature. As for the radiator, it's not even remotely related.
Normally the "heater core" means the heat exchange component. Where the heated coolant flow thru and heats it up. It's not common for it to fail.
The "heater unit" encloses the "heater core" and has some mechanisms to control certain doors to route the air flow. One door called "air mix door". Which controls how much air flow thru the hot/cold side. That could be the culprit. If the motor is dead, or some component failed, leaving the door stuck open for cold air, then you have no heated air.
When I said the blower assy, I actually mean the heater unit, since they are kind of all connected together. The heater unit is located inside the center console. It's not easy to access or repair.
Hope the explanation helps and good luck.