ActionScript 3.0 :: Syncing Externally Loaded Audio Files?

I've developed an application which uses a (dynamic) XML file to load in several files; a maximum of four MP3 files and a number of JPG files.When everything has finished loading, the user can press a "Play" button. The application could be described as a "mixer"; it's used to give online music lessons and to facilitate this, the sheet music is loaded (cut up into into several JPGs) which move horizontally on the screen like a marquee, while the music it represents begins playback. The music exists of several MP3s so that the user can mute (e.g.) the vocals or the drums, allowing him to focus on (e.g.) the guitar.

So what's going wrong, is that the audio files are not playing in sync. They are all pre-loaded so any delay between files shouldn't be sought in the files not being fully loaded yet. For initiating playback in the application, I'm using a simple function with a for loop in it, which sets each instance of my sound class to start playing at position 0 of its timeline (I've added in highlighting for all of the "code" blocks in my post, to keep everything easy to read through):

Code:
function playSounds():void {
for (var iCnt:Number = 0; iCnt < aSound.length; iCnt++) {
// Start playback for each sound, at the time position set in the

[code]....

Seeing as this didn't work, I have no clue what I could give a shot next... so if anyone has any ideas or suggestions, it would be greatly appreciated! Something else I noticed, was that if I run the application on very fast PCs, the MP3s are almost always in sync, but the PC that I'm developing on isn't that sluggish either and they hardly ever run in sync on it - so it will form a problem for pretty much all of the people who will use the application.