Theft light flashing and radio problem

I was just given this 2001 explorer sport 2 door so I'm new to this model. The theft light flashes slowly when the vehicle is off. It starts fine. Can I turn this off? Is it supposed to stay on all the time when the vehicle is off? The other issue is the radio. in the morning when I start it up the radio won't come on. As I drive to work it's dark and I can see the lights in the light in the radio dimly flashing and it won't come on. By the time I get to work (around 25 minutes) the radio starts playing. The time then has to be reset. In the afternoon it seems to come on with no problem (mostly). Could these be related? Any ideas where I should start trouble shooting? I was thinking a loose plug on the radio. I can only hope.

*UPDATE*

The dealer told me the Theft light was a normal function to flash like that.