I expect the radio going dead is another symptom that something is happening with the 12v power, and not the cause. If the radio was shorting the power, the radio fuse should be blowing. It's likely when the power is fluctuating the transmission goes into limp mode, and that is why you cannot shift it.

As the others have said, you should check the battery cable connections. Make sure they are clean and tight on the battery, and on the other end of the cables.

If you still believe there is a link to this problem with the radio you can either remove it, or remove the fuses supplying power to it in the fuse box in the engine compartment. Your owners manual shows where they are.