It could also be a battery cable issue

It could also be a battery cable issue, may also clean the battery negative post, use battery terminal cleaner. Check the connection of the other end of the negative cable – normally goes to body of engine or starter. Hope is not the starter problem, check battery voltage when engine is Off (>12.5V) and On (>14V), check all cable connections.

Also I have a question to you, did you find out the root cause of the suddenly radio turning On problem? I have the same problem on Accord 04.