I received Rhianna's 'Good Girl Gone Bad' CD for my birthday, and I listened to the whole thing. Disturbia was... disturbing. When I listened to it bad words would pop into my mind like 'Death' or 'Kill' or others I can't think of at this moment. I stopped listening to it immediately, threw away the CD, called it a day.
I also received the same vibe when 'Run This Town' came on the radio. It was extra-sensory in a way that I truly can't describe. I knew it wasn't a good song, so I shut it off ASAP too. A few days later, VC cranked out a video analysis of the song and I commented saying 'I KNEW IT! I'm not crazy!!!" lol.
But yes, I do believe secular music can have demonic influence. Heck, all music has some influence on us--it's all dependent on what we listen to.