Background noise with Creative MP3 Player

So I got the Koss Spark-Plugs (which are awesome, thank /g/ for the advice) which has increased the quality of Player->Ear transfer a lot.

I own a Creative Jukebox Zen Xtra (60GB), and now that I hear the sound really well I also hear a really irritating, high-pitched, noise whenever the screen is not lit up. As I listen to music which is often quiet at places (post-rock genre, Devil Doll, etc) this becomes extremely irritating.

Has anybody else experienced the same thing, know what to do about it?

I have heard the high pitched noise on my player (Archos something or other) when the screen is lit up, but never while unlit. 

It may be your player.  You just never heard it because your previous headphones couldn't relay it.

Try returnng the headphones as defective. If you still have a problem then the player is your problem. Return the player or get slightly worse headphone for it.