using a volt meter will help. set the voltage to A/C.
do this only if you have experience. I'm not responsible if you shock yourself. take the cover off. look for the relay by the output transistors (look to see if they are burnt too, while you there). turn radio off and on. the relay should make it own clicking noise when it turn on. sometime just flicking it with your finger will temporary unstick a stuck relay.
if it's the relay, take it to the shop and tell them to replace it. a relay cost them 5.00 plus labor. if you don't tell them the problem, they will tell you that your transistor are bad and charge you a lot of money to fix it.