Either a broken wire - faulty switch - or bad ground. You're going to need a test light to find the fault here. Is there power to the hot side of the blower switch? Does power transfer to the cold side when the switch is turned on. Is power reaching the blower. Blowers rarely fail BUT it can happen.
where is the blower motor on a 2001 chevy blazer
The fuse. The blower motor speed resistor. The blower motor relay. The blower motor switch. Check for power at the blower motor connection.
how to change the blower motor
Blower motor NG. Blower motor resister NG. Blower motor fuse NG. Blower motor switch NG.
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.
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.
Under the hood, passengers side firewall, close to the blower motor.
probably the blower motor resistor
The blower motor relay for high speed would be located in the power distribution box under the hood.
Should be behind the glove box. The blower motor speed resistor is located under the hood, on the firewall, passenger side, close to the blower motor.
on the fire wall on the passenger side
Passenger side firewall near oil fill for the motor