Sounds like the permanent live and ignition live have been swapped round, which is the usual when fitting after market stereo's.
The black iso plug should be in 3 sections stuck together, the top row is the longest, containing the changer connections and the multi display wires, the middle row is for the speaker wires (runs to the amp on your car) and the bottom row is the power wires etc,
if all this is correct, then then swapping the wires back to where they should be will allow you to plug the std unit in.