If it picks up AM and FM stations then you can safely assume it is working. The concept of "My radio works fine except the shortwave part is broken" is very unlikely, although I suppose technically possible. Your problem is reception.Or is this radio not working?
Stream it on the web with much better sound quality here: http://bbcworldservice.radio.net/I was hoping to listen to a bbc channel. does bbc broadcast 24 hours a day ?