Why won't my battery turn over when using accessory power?

What is your question?

If I sit in the car and listen to the radio even for 5 minutes or have the keys in the ignition and door open when loading the car, the battery drains completely and I need to get a jump start. All other times the car starts with no problem. Also, there's a constant humming like something not turning off coming from the cigarette lighter and it's never used. Thanks!