Hola Marc

Even if the radio is irreparable, you still use "está estropeada" (not es estropeada) as it's talking about a physical condition and a result. The fact that it may not be possible to fix it doesn't really matter. When we use "ser" with adjectives we express an essential characteristic of something or someone: "yo soy alta" (I may shrink a bit when I get older, but that doesn't matter, being tall is one of my essential physical characteristics, hence "soy") 

Saludos cordiales