Radio coming on when car is off and locked

As the title says, I occasionally come out to my car after it's been off and locked for a few hours or over night. And the radio is on and playing. If I leave it on aux setting when I turn the car off and I discover it's on, it goes to the radio everytime.

Earlier today I came out to the car and the battery was flat. Nightmare.

I've searched for ghosts but no luck. Help!
 
Bit the bullet and replaced the battery as I'm pretty sure it's the original item. Hope it fixes it.

On a side note, when I pulled the fuse under the steering wheel labeled radio. I could still turn the radio on and off but I only lost a/c and rear heated screen functions. Is that normal or?