There is a blog here which explained how to create a Media Player in WPF :
Do check out its second part.
Also after having a quick review of the code that you provided,
Add these events too :
1) MediaOpened : to set the isPlaying to true
2) MediaEnded : to stop the MediaElement by providing MediaEL.stop()
3) Set the LoadBehavior to Manual
4) UnloadedBehavior to Stop
The blog has the complete solution, check out its second part too : http://www.studentguru.gr/blogs/dante/archive/2011/01/12/122329.aspx
All the best.