What could cause the air conditioner not to blow air?

If it's not blowing ANY air at all, you either have a defective blower or severely clogged ducts. If it's not blowing COLD air, there's a vast number of possibilities for why this might be, ranging from low refrigerant, bad sensors, blockage in the AC system, a faulty compressor clutch, damaged fins on the condenser, etc. I'd recommend you have a qualified professional do a system performance test on your AC system.