Why is there a tick, tick, tick sound coming from uner the hood of my car?

I have a 2003 Grand Prix, low mileage (36, 435) runs well. I notice
two days ago, a ticking sound coming from under the hood when I
turn the car on and off. I had pulled up to park and that's when I
heard the ticking sound. It continued to tick for about 5 minutes  
(the engine was off) and then it stops! I also smelled rubber
burning as I got out of the car. I am pretty sure it more like, tick,
tick, tick...than a "ping" sound. I had an oil change in July 2017,
fluids checked, and the ignition switch was repaired in July as well
(it would not turn all the way off, the key would get stuck and
would not come out, the battery would be dead the next morning
because the (P) parking light on the dashboard was still on.  My
neighbor said I needed a new battery. It does not crank up
immediately in the morning. When the car is driven for a few
hours, it starts up quick.