The failure Zeronero mentioned above was probably caused when the compressor controller "sensed" a difference in speed between the compressor (which would slow down with a slipping belt) and engine crank speed. This is a failsafe system that disengages the magnetic clutch because the differences in speed between the compressor and engine is assumed to be because the A/C compressor may be mechanically failing and seizing up as it fails. As it seizes, it will stop rotating, even though the engine attempts to continue running.
The HVAC blower motor is not tied to this failsafe circuit; so, the blower should continue to run even if the A/C compressor has been disengaged. The fact that the blower no longer works is more than likely due to a defective switch in the A/C control module, or to a failure of the blower motor. In my three failures, 100% were due to motor failure!