Sounds like Firefox either isn't allowing the plugin or is having problems with it. Try uninstalling/reinstalling the plugin, paying special attention to any popups asking your permission to allow installation.
Nothing against Firefox, but have you tried it in Safari ? Just curious if that might be a quick workaround while you're getting Firefox up and running.
Here's a support doc with the relevant instructions:
An alternative I prefer is to use the full Mac SlingPlayer instead of the limited Web Player. If you don't have a copy, grab one here and give it a try. You might like it.
Hope this helps,