Unfortunately for you, at the school where I work, headphones/speakers were the fix to this particular problem. I'm still looking for other solutions that don't involve older versions of Firefox and/or Flash.
Update: I fixed the problem permanently by installing the actual sound card drivers instead of using the Microsoft High Definition Audio drivers. I have a Dell so I just went to their site, put in the service tag, showed all drivers, downloaded the SoundMax Integrated etc..., extracted with 7-zip to a directory and updated the drivers manually. Works perfectly in Firefox and IE now (never stopped working in Chrome).
Good luck!
