The video backgrounds relies upon the webkit backend. (regardless of what you set up in the settings i.e. VLC or Phonon)
Try change your preferred backend to webkit, and then try sending a video live from the media manager. If this works and the background video doesn't please submit a debug log to support (at) openlp (dot) org (see http://manual.openlp.org/faq.html#i-ve-been-asked-to-email-a-debug-log-where-do-i-find-this)
If neither works, and assuming you are on windows, installing a codec pack may help, and will let you play lots more video formats. (search the forums, or use Google to find one.)
Once you get this working you can switch back to your preferred backend.