Videos already on the computer are played via a media player (such as Windows Media Player, VLC, GOM, or whatever else your daughter uses). Streamed videos are played within a browser using the Flash Player Plug-in, which has an annoying habit of ceasing to work.
Go to Add & Remove Programs (or Programs & Features, depending upon the version of Windows), from the Control Panel. Locate and uninstall 'Adobe Flash Player Plug-in'. Restart the computer. Go here to reinstall Flash:
http://get.adobe.com/flashplayer/
(NB: Remove the tick that installs McAfee Security Scan Plus before clicking on 'Download'!)
That should solve the problem.
Chris