The shriek is probably feedback being caused by a dodgy capacitor between the DAB and FM tuner and the amplifier section. Impossible to diagnose further wirhourt a circuirt diagram.
The amplifier,section must be okay because music is playing via Bluetooth. The tuner section is okay because you can hear stations in the background. Therefore the fault must lie between the tuner and amplifier sections. Electrolytic capacitors are the components most likely to fail. They look like little plastic cans stood on end in the circuit board. The exact value for a replacement is generally not critical (+ or - 20%) just so long as it physically fits and the voltage rating matches or exceeds the original.