Coolant overflow

I assume that the tank is overflowing, without adding any liquid. Is the fluid oily? It sounds like you most likely have a transmission oil cooler(internal to radiator) leaking into the cooling system. This can be a real problem, as by now the oil has completely coated the cooling system. What happens is the oil attacks and softens the rubber. If you opted to replace all the hoses and such, it is prudent that you thoroughly flush the cooling system to remove as much as the oily residue as possible, or the new rubber will soften over time.