If your vehicle doesn't have an electronic climate control system (push buttons, auto temperature, etc.), it's probably one or two blown power resistors. Here's how this design works:
You have a 4 position switch at the console for fan speed--low, medium-1, medium-2, high--and a series of resistors--R1, R2, and R3.
In the low position, current goes through R1, R2, R3 in series to the blower motor. In the medium-1 position, current goes through just R2 and R3. In medium-2, current goes through just R3. Finally, in high, it's full voltage to the blower motor via the blower relay.
It sounds like you've blown R1 and/or R2 (if you have the regular climate control) which means you have to replace the resistor assembly.
However, if you've an electronic climate control system, it probably means you'll need to replace what's called the "Blower Control Module"--which is basically a solid state power transistor pack.
Either the resistor pack or the blower control module is typically inside the passenger compartment--usually near the front of the dash near the blower motor or evaporator housing.