The play button only works for the playlist. If you want to play songs that are in your library but outside of the playlist function then use the Launch button. If you wish to preview a downld then use the Preview button (but you can only preview as much as you've downlded.) For the playlist you use the Enqueue button to move songs over to the playlist function. You can only play what you select!!!
If you've tried these things & it doesn't work. Disable LW's media player so your default audio player works instead. To do this, go to LW's menu Tools>Options>Player & untick option box & press apply. You'll need to wait until next time you open LW before it takes effect. Hope this helps!