That broken radio is where The team rocket leader Giavonni was training a while back. If you get the event Celebi, then you'll be able to go back in time to discover that your rival Silver is in fact his son. He left his father and called him weak since team rocket recently fell at the hands of a kid (the character from Red/Blue/yellow/FR/LG) so he stays there to train.
When you go in the cave, you'll see Giavonni there and you'll here a few rocket members contact him saying they're ready for his return. After a brief battle with him, he'll be crushed that his training was for nothing and that he lost again to a kid.
Since he just left it there, the Radio aged for about three years. There's nothing you can actually do with it, it's just there because of the Celebi Event.