My A/C unit ices up and then won't let the blower

If this unit has an intergral thermostat and the option to run the fan on lower speeds, the unit WILL freeze up when you operate it for long periods of time operating at minimum temp setting and the fan running on one of the slower speed options. This is not an unusual occurance. Solution: run the unit with the fan at maximum speed or dial the thermostat so the compressor has a chance to cycle while operating on lower fan speeds.

Low refrigerant charge sounds like. you will need to have the unit serviced

The thermostat is faulty or out of adjustment. Replace it.