Check the battery with a multimeter. With the car off, it should read 12.0-12.5volts.

Then, check the battery terminal connections. They should be clean and tight with no corrosion.

Then, with the car running, check voltage across the battery again. It should read 13.5-14.5volts, standard alternator output.

A weak alternator will undercharge the battery and cause all sorts of low voltage related issues (such as the car not starting or the radio cutting off.) Ignition switches, especially in Hondas, rarely go bad.