I also posted this response in your other thread;
I suggest this as a quick check of the converter. Measure the voltage at the battery without shore power connected. Next, plug in the shore power and check the battery voltage now. Usually, the measured voltage will be a bit higher, like one volt, with the converter operating and charging the battery. If you have a helper, you can monitor the voltage at the moment shore power is connected, and see the rise as it happens.
As for the radio, I don't know if there is a fuse right at the radio, but it's possible. You may try measuring for 12 volts at the back of the radio, which would require removing it from the mounting.