The fan does not turn on when I turn the car off

The clicking noise you heard was the fan relay. There is a control box on the right side of the heater box that controls the fan timer which runs the fan a certain length of time after you turn of the car. First try replacing the cooling fan relay which is next to the cooling fan. Then there are two other relays, replace the one for the condenser fan the other for the A/C compressor clutch, do not get them mixed up. You can trace the wire from the compressor to the relay.
Relays are pretty cheap if you buy them from the right place. Go to www. Carrepairlinks. Com and it is a good site for finding reputable retailers and will tell you which ones are cheapest and usually has discounts if you order through ad banners on site that you cannot get otherwise.
After replacing all the relays if it continues it is the fan control box. You might try to get one from a salvage yard first as they are a little more in cost, but you might find a good deal on one of those as well.