Radio/tape Cd Player problems of the 2004 Chevrolet Impala

Tried to start car, wouldn't turn over even though car had power, no noises or sounds made when trying to turn over even though I had full power to radio winders doors and electric dash board. Had a new starter put in because I thought that was the issue. 2 weeks later security light comes on while driving and stayed on. Tried to turn car on same thing happened have power. But no turn over and security light is still on. Turned off car took out keys and left car alone came back later and car started w/o incident. No security light on. Same issue keeps happening maybe 4 times a month if not more have to wait 10 mins in order for car to start. Issue happens at gas station, home, work, hot and cold weather. Before I figured out 10 min delay had car towed and spent money on repairs that aren't necessary. Noticed one day while I sat in car for 10 mins in summer heat with 3 month daughter, that car makes a sort of computer humming/buzzing sound. After the 10 or so I hear a click or as I call it a shut down sound and then I am able to start car.

Every now and then you go to start the car it won't do anything. All the lights, radio, everything comes on as normal but when you turn the key over to start it won't do nothing, click, or anything. One time we left the car over night, locked up, the next day it started like nothing was wrong. Another time I let the car sit for 15 mins and it started fine. Then another time, I kept trying every 10 to 15 mins for an hr but nothing. Then let it sit for 25 to 30 mins then nothing but I left the key in on position for a couple minutes while all the lights ran and then it started fine. Some people say its the starter, ignition or even the security. A lot of people have had this problem there's even videos of people complaining. Id say that there's something that needs to be looked into so everyone w these vehicles know what's wrong. Thanks.