Stock or Aftermarket?
Is the radio stock, or is in an aftermarket unit? There may be more fuses to worry about with an aftermarket head unit than the fusebox. Rather than getting a voltmeter, you can also use a cheap test light. One end to the wire, the other to ground just as black car suggested. Rather than reading volts, it will light up with the ign switch turned on. If it doesn't , you need to follow the wire in question to its source, looking for other fuses or possible wire taps in other circuits that may have blown other fuses or bad connections.
As I recall, the factory units had a problem with the power switch on the radio, so if it is a stock radio, this may be a possibility if you confirm power at the wiring is OK.
The black wire may be a ground. Use a known 12v source and connect the other end of your test light/meter to your mystery black wire. If you read volts, it must be a ground! If no volts, try every ign switch position. If still no volts, do the same thing but with a known ground.
Good Luck!
