Something must not have went back together correctly when replacing the heater core. Looks like someone has to do the job over again.
blower motors bad check fuse bore replacing
Motor hasseized.
A short.
Did you chech the fuse?
Heater blower motor is defective and locked up, or possible short in the wiring.
check for a blown fuse that says heater or blower motor
If the heater fan is not blowing on a 2001 Chevy S10 Pickup, it is possible that the fuse needs replacing. It is also possible that debris is interfering with the operation of the fan. Could also be, a faulty fan motor, a faulty fan motor speed resistor, a faulty fan motor switch,
The fan motor has a short...change it.
You should check the thermostat and the fuse for the heater.
Fuse, switch, speed resistor or motor.
You have a short somewhere in that circuit if the fuse blows soon after replacing it check the condition of the wires in that circuit
there is a short somewhere in dash or heater, you need to fix that to stop fuses blowing