Short in the circuit somewhere. Try unplugging the blower motor, closing the circuit with a test lead or test light, and seeing if it blows then. If not, the problem would seem to be in the blower motor itself.
where is the blower motor on a 2001 chevy blazer
how to change the blower motor
You didn't mention what year S10 Blazer you have but, the blower motor speed resistor can be found under the hood, on the passenger side of the firewall, close to the blower motor.
probably the blower motor resistor
Blower motor NG. Blower motor resister NG. Blower motor fuse NG. Blower motor switch NG.
The blower resistor gets overheated and burns out usually because the blower motor is failing also.
They get noisy, squeal and vibrate. Also if you keep burning out the blower motor resistor, that is a sign the blower motor is on its way out.
Under the hood, passengers side firewall, close to the blower motor.
on the fire wall on the passenger side
Ain't no fixin it, you have to replace it with a new one.
Passenger side firewall near oil fill for the motor
its under the glove department. and if its like my blazer under the little shelf like thing under the glove department.