2004 Ford Taurus starting

On 3 different occasions I put my key in the ignition turned it and everything was dead there is a ticking noise sounds like a turn signal even thou nothing was on. It will continue the ticking noise even after I remove the key. I turned on my headlights to see if the light worked of if I truly had a dead battery but when they were turned on the car started immediately and then works fine for who knows when then it does it again no cause. Last time it did it (last night) I had cut the engine off and left my head lights on the ticking noise started and I turned my lights on again and the car started right up. When it does this it sets the clock back to 12:00 and my miles to empty mpg back to 0. Other thank this there is nothing at all wrong with the car, I just put new tires and battery on it in June. Any suggestions?