Not Starting after turning off

Hi! Im new here and am having a problem with my Kia. It has so far been a good car but recently within the past week while I am driving, the radio (which I had installed a few years ago professionally) will turn off and on. When I turn the car off it wont start it will just click like the battery is dead. All interior lights and headlights still work. Well a few days and a new battery later it is still doing this off and on. When it does even with the new battery it has to be jumped to start. My husband has tested the battery and volts the car is giving out and it all is ok. Anyone else have any problems like this? Oh, I forgot to mention about a month ago a coke can exploded in my car but I havent had any problems until recently. Its just making me crazy because I never know when it will happen and am scared to drive it because I might get stuck! :uhoh: Thanks!