Why will the car cut out while driving it and the radio will not turn down?

It sounds like you have two separate problems. The power issue may be a bad connection between the panel under the hood and the ignition switch. I assume the battery connections have already been cleaned and snugged tight. The trouble could also be with the ignition switch contacts. The radio problem is most likely due to a problem inside the radio. If there is a external volume control then that could be a possibility also.