Thanks for your polite support request. :-) I've taken a look at your site and the thing that's jumping out as the most likely culprit is jQuery conflict. You have a lot of functionality that uses jQuery and I can see in the source code that the page is calling a bunch of different versions of jQuery which often causes problems.
All WP plugins and themes really should be calling the jQuery scripts that are included in the WP core, they shouldn't hard-code their own jQuery calls... but I suspect several instances of this on your site.
Did the player work when you had all other plugins disabled?
If so this would isolate the issue to another plugin.. which you can then isolate further to a specific plugin.
Does the player work if you switch to the standard twentyeleven theme?
If so it would indicate your theme has hardcoded jQuery...
Try running a debugger to isolate any script errors... post the error messages back here so I can check them if you want.
Sorry it's not an easy solution... all I can say is that 10,000+ other users have it working fine in all browsers, so therefore it is very likely the problem is something specific on your site. We just need to go through steps to isolate exactly what the problem is.
Again, sorry I can't be more helpful - you'll both just need to work through all the possible causes in order to isolate the error.