Heater won't turn off
There are two possibilities. The ON-OFF switch is bad or your blower motor resistor is bad. Typically, when the resistor fails, you either have no power to the blower motor, or you only have one fan speed. I have never seen one go bad where the fan was always on. I would be more suspect of the ON-OFF switch. Not sure what year you have, but you may have to replace the whole climate control unit rather than just a simple switch. Try Ebay or your local salvage yard.
Search Chevrolet Blazer Questions
Chevrolet Blazer Experts