It's a long time since I had the questionable pleasure of dealing with one of these... However, they are basically just a tank with a float-operated pump. Your continuous noise will be coming from the pump, and this is bad news not only because it means the tank is not emptying but also because these pumps are designed to operate in short bursts rather than continuously. So the first thing I recommend is: don't flush the toilet again until you've got the blockage sorted. Second: switch off the power to the unit (if it's wired in to a wall outlet without a switch, remove the fuse from the outlet). Third: locate the place on the outlet pipe where you think it may be frozen, wrap some rags around it and then pour hot water on it (the rags will help retain the heat). Remember, you are melting ice, so this may take some time and several applications to be effective. From time to time, switch the unit back on to see if it's now draining. Once you get it clear, you should lag all exposed pipe that may be liable to freeze. While the freeze continues, you may also like to consider flushing with a bucket of warm water rather than using the cold cistern! Good luck! P.S. I don't recommend using antifreeze.

Further to this adice - you should consider the following. If the saniflo is trying to pump upwards for instanc into loft etc, as soon as you turn off the power the pump will stop and the mass of water in the vertical section of pipe WILL come back down. It will also come down with a LOT of PRESSURE. MAKE SURE YOU ARE WEARING GOGGLES / Something over your face and mouth... I speak from experience. I am also trying to defrost a 50m length of waste pipe.

Not a solution but there is a cap on the top of mine. I have just poured two hot kettles into this hole. Still frozen at the minute though. Mine pumps very little height and straight through outside wall. I think mine may be frozen inside the unit.