1996 Oldsmobile Achieva Engine overheats at idle

If I am at idle for a long period of time, the temp gauge willl start moving from 1/2 to 3/4 to the hot side. I have replaced the coolant, water, thermostat, cooling fan, water pump, water pump lubricant. I have done a master flush on the unit. When I see this, I have gotten out of the car to check the cooling fan. It is not working. If I turn on the air conditioning, the fan will come on. The temperature will go now to normal. This car requires the computer and a sensor to come on together for the cooling fan to work. I need to narrow it down to the following: fan relay, fan sensor, gauge sensor, radiator, and potential blown head gasket. Give me the potential problems in order of expense.