Hold off on cutting any wire wraps just yet.
Just out of curiosity do you have a yellow wire off of the new CD radio, a red wire off of the new CD radio, and a black wire off of the new CD radio ?.
Where exactly and to what colors are these wires hooked to in the car ?
At the radio opening in your car there is a 3 terminal plug with a gray, a black, and a yellow wire in it. The yellow off of the car DOES NOT connect to the yellow on your new CD radio. The red wire off of your new radio will connect to the yellow wire in the cars radio harness, the black will connect to black and the yellow wire off of your new CD radio can either be connected to the cigarette lighter wire (orange) or can be run to the fuse block. Some radio's will not work if there is no power on both the yellow and red wires.
The more I think about the problem you are having I'm wondering if it's something as simple as a hookup you have and everything is right on one circuit but we are troubleshooting the wrong one. In other words you blew the radio fuse in the fuse block but currently there might not be power on the second power wire of the radio and it does not work (when it was tested on the battery you should have had the yellow and red tied together and these two going to the positive post of the battery and the black to the negative).
Jim