If the Play button is not showing up in Firefox 3, try these steps:

1. Do you have the Adblock extension installed? In Firefox 3 Adblock incorrectly blocks Flash content, even if your entire page is whitelisted. In this case just disable Flash block. Or use Adblock Plus instead.
2. Just make sure that you have the required minimum version of the Flash Player installed.
3. Ensure that you don’t have a corrupt Flash Player by uninstalling the Flash Player using the Adobe uninstaller and by reinstalling the plug-in via the Adobe Flash Player installation page.

Taken from the WordPress Audio Player Troubleshooting page, which stole it from the swfobject 2.0 FAQ page.