Screen Saver Mystery when using Windows Media Player?

Here's my dilemma. I enjoy listening to talk radio via the Internet and my current vehicle for this is Windows Media Player. When involved in any other activity using my computer, after a few minutes of inactivity my screen saver kicks in like it is supposed to. But not so with Windows Media. It just stays lit all night long. I've even tried minimizing it, but to no avail. The screen saver will not kick in as long as I'm tuned into my radio station of choice. What is up with this? Is there anything I can do to activate screen saver while listening to the radio so that my computer is not functioning as a "night-light"? Otherwise, I am content with Windows Media Player. Thank you.