Do they play if your phone is connected to the PC and you navigate to where they are on your phone using it and try and open using Windows media player? I ask because I'm trying to rule out any problem with the actual file.
These songs have moved from every android phone I have ever had starting with the moto droid via my sd card. Never had any problems playing them till I switched to my note 3. That's why I think it is the phone and not the songs themselves.
Give PowerAmp a try. There's a trial version in the Play Store, $3.99USD to unlock to full version but worth every penny. PowerAmp specifically supports mp4/m4a (including alac) file types as well as a bunch of others including wma.