Is the sound file embeded?
Is the file uploaded?
The audio files have been uploaded with the swf, in the assets folder. I'm not sure how to embed the audio into the project. Is this the best thing to do?
What did you upload to your web server? Be sure you've uploaded the entire "deploy-to-web" folder's contents without any modifications. (Including any subfolders, which must stay as subfolders).
One thing you can do is use a network monitor tool to see what URL your project is looking for the audio files at, to make sure it matches where you actually uploaded the files. If you have Flash Builder, there is a built-in "Network Monitor" tab. On Windows, there's also a free tool called Fiddler. On Mac, I believe there are several free tools as well.
Or, if you post your URL here I can check it out using a network monitor tool on my end and then let you know what I find.