You must live near a radio station transmitter. This used to happen all the time when I worked at a 50,000 watt AM in Oklahoma City (KOMA). That station could literally be heard on toasters. It's amazing what can demodulate an rf signal. The old story of someone hearing a radio station on their fillings is absolutely true. It happens with lower power transmitters as well like CB and ham radio. In fact, it's pretty common. The problem is that your receiver isn't shielded very well. Don't worry, most arent. I'm surprised you aren't picking it up on your telephone. My 100 watt ham radio used to get into a neighbor's VCR.
Don't mess with Faraday cages. It's a waste of time and it's ugly. You need pretty fine mesh and every seam has to be sealed extremely well, meaning you won't be able to get to the plugs on the back or the controls on the front. Faraday cages are for rf engineers, designers and technicians.
The fix is cheap and easy. I put a filter on the output of my ham radio transmitter and it cleared it right up. Sorry, the radio station won't do that for you. Go to RadioShack and get some
toroid chokes and put them on both speaker wires and the power wire. That should take care of the problem. The dweeb behind the counter probably won't have any idea what toroids are so just go directly to the parts drawer and start looking. You can also order them online. RadioShack... you've got questions, we've got blank stares.
Let me know how this works. I think it will solve your problem.