I am experiencing unprompted radio scanning while listening. Also no climate

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control upon starting. The radio issue corrects it's self after I power it off then on again but this is not a permanent fix. The Climate control is also a random issue. When the car is started and the AC was left on it whirrs into action. But if the AC is off when the car is cold started it may not come on at all. I will push buttons and nothing for a few miles. I have taken it to the local dealer and they can not make these things occur after an over night stay there. I have also experienced a no crank no start situation a couple of times with a new battery. The battery tested bad so that has been replaced. The Pathfinder start up as expected but not sure if it is getting a charge from the alternator or not. Is all this related, what is the process of elimination in these situations. Thanks