Why do neither my heater or air con work?

Without seeing the condition of the car, it's hard to make specific suggestions on what you should do. I'd start by first checking the coolant level, as that will affect the heater core. If levels are good, let the engine warm up to temperature, then check the heater hoses, they should be warm/hot, and pressurized. If not you may have a blockage in the heater core (this is also assuming the engine's cooling system is working as normal). If it seems as though the heater core should be getting hot but isn't blowing hot air, then check that you don't have a "temperature blend door" stuck open to the AC evap coil. Blend doors are plastic flaps that direct incoming air from the blower motor fan across either the heater core OR the AC evap coil. A small actuator moves it based on your temp selection. Move the temp selector, you may be able to hear the door swinging and/or slight pressure change in the incoming air. Then you have to consider the non-working AC. That can be from any number of causes, from loss of refrigerant (needing a recharge) to a non-working compressor or some as yet-to-be determined problem. Don't waste your time/money on those "AC Pro" recharge kits, go to an AC repair shop and have them diagnose your heater/AC problem.