@Nancy,
In case you're using Internet Explorer or Google Chromeor Firefox for playing those games, then do like this. When you start playing the game on any of the above browsers, you will start listening the sound of that game. At that point of time, go to System tray, right click on Speaker Icon and select Open Volume Mixer. There try to mute only the browser speaker, on which the game is running.
Now go and play the Music using any of the Player to see if it works.
Keep us posted if you require further assistance.