Why don't your dome light come on?

Check all the fuses first, if they're fine,
For the radio(if it's in fact the whole radio and not just the head unit light); check the fuse on the back of the radio if it has one, check for current from Battery+ wire leading to radio, or ground. if those check out fine, the radio itself is most likely dead, if nothing had power it could be a relay on the printed circuit board(don't touch this with your fingers), have a technician diagnose this.
For the dome light; check current to the switch, if it checks out fine move to the light itself, if it checks out fine replace the bulb, if there is no power at all it could be a relay, or a B+ wire is shorted out, or the ground isn't good.