I have the same problem and I replaced the said adapter with an off the shelf 12v adapter and at least the radio plays now.
Reply: Black And Decker - FS18RC Adapto...
YOU WILL HAVE TO GO TO LOWES AND GET A NEW CHARGER FOR $32.00. THAT IS WAY THEY DON'T HAVE THE REPLACEMENT PART. THEY MAKE MORE MONEY SELLING A NEW CHARGER. I'M LOOKING AROUND AT YARD SALES FOR ONE OR LOOKING FOR A 18V PEACE THAT PLUG INTO THE WALL AND SPLICE THE OTHER IN INTO IT. HARVEY