Agree with the previous post. Some sort of short/wiring issue. I have seen this in computers and laptops. Liquid or even humidity does REAL damage to electronics. Especially that this is the outside radio/tv.
Had a laptop once where the owner swore they never ever spilt any water on the laptop. They were complaining it would all of a sudden start typing random characters and even shut off by itself.
Never ever did they have any water in it!
Took the puppy apart and there was dried up coffee in the keyboard and worked it's way into the main board.
Never ever did any water spill in it. Never. Really.
So, may be time for a new radio. Maybe it's just the remote. See if you take the battery out of the remote see if it randomly starts then.