All I wanted was to put one soundtrack music on my blog and keep the music playing during the navigation without stopping it when clicking on other page.
There isn't a way to do that on WordPress.com.
I read there are some free plugins that makes it happen.
WordPress.com has pre-selected plugins and you cannot install them yourself, but if you could find a plugin like that then you could set it up if you did switch to WordPress.org. You don't need to purchase the Guided Transfer option, you can do it yourself! But you would need to use the volunteer-based forums at http://wordpress.org/support/ to get support if you don't want to purchase Guided Transfer. The community is great! But it is volunteer-based, so if you ran into trouble, you'd need to see if someone would be willing to help you out for free over in the other forum. :)
You might start out by searching the plugin directory at http://wordpress.org/plugins/ or asking for help with your plugin search at http://wordpress.org/support/
On WordPress.com, you don't need an upgrade to play music, but you do need the Space Upgrade if you want to upload mp3s to a WordPress.com blog yourself. If you have a link to one available on the internet, you can use the regular audio player:
It won't continuously play between different page loads though! For that, you'd probably need a more custom setup like a WordPress.org install with some custom code added.