[Mr. C.]

Hi, I believe that you should trouble shoot your problem based on the reaction of the "battery" light and put the radio reaction aside for now. The radio is an unknown and using it to diagnose means you have two unknowns working.
So how does the light work with the radio off. Remember that the light is a charging indicator. If you have more current being produced than is being used, the light cannot light. If you are using more than the alternator is sending to the battery the light comes on. If the light comes on with the radio out of the picture, your alternator is not creating enough current or the regulator is not allowing enough current to go to the battery. Once the engine is running, the alternator should supply the current needed the battery should not need to supply any and the light should stay OFF.
If the light does not behave properly with the radio out of the picture, forget the radio and have your charging circuit checked.
The regulator is most often the problem but not always.
If the light works OK with the radio off, the alternator is not creating enough current to supply everything. Now you need an ammeter. You need to determine if the power produced is too little (<30 amps) or the power needed is too much (>30amps).
I have used a lot of words to say the same thing as others (alternator/regulator output is too low) but I think it is important to understand what is happening. The radio could be simply overloading the alternator. 50 watts for the speakers is 4+ amps, a couple more for the CD motor and you are using 6 amps.
MrC