Look at the "Power connector" on the back of the radio - it is the larger one with eight flat pins. Counting from the top ("key" notch is at top of plug), count the pins from top to bottom as one thru eight. The Power amp turn-on is at pin #8. You need to move that wire so that it mates up with pin #4 (Power Antenna signal) of the radio.
If your connector (harness side) has a red "locking spline" in it, that will have to be removed (temporarily). Pry it loose with a small screwdriver, tweezers, or awl. Once the locking spline is out, the pins can be removed from the connector. Your pin location #4 should be blank (no connection). Using a paper clip (or very small screw-driver) release the pin (they usually have a small retention tab) from the connector at pin location #8, and move it to location #4. Push it in to the connector until it "clicks". Snap the locking spline back into place, and you should be all set.
I thought of one other thing it MIGHT be, but not as likely. Some of the Premium Cassette radios were made to be "CD Changer compatible". If there is no CD Changer in the vehicle, then they need a "shorting plug" installed in the top (6-pin) shielded connector spot. This is easy to check - just add the shorting pin (it is a plug-in connector), and, if the radio then works, that was it. Without the pin, you will have no audio.
Either one of these situations (shorting connector or amp turn-on voltage) could cause the problem you've described. Good luck fixing it, hope this helps.
Regards,
cobrajeff