well the power source for the radio comes from two sources in the car. The first is the permanent live, usually a yellow wire, which is the fused power source that comes straight from the battery via the fusebox. This is what gives the radio power and its memory to store radio stations.
The second is the ignition live, usually a red wire, which is a feed from the ignition switch that tells the radio to switch on when the keys are in the ignition.
The radio needs both of these to function. If the fuse hasn't blown, you should find the pernament live gives 12v no matter what. The ignition live should only be 12v when the ignition is on. If its in an old VW, the ignition switch can fail, and will stop your radio switching on.
Have a look at the wiring with a multimeter if you are definately sure you haven't blown a fuse