Without knowing exactly which site you're referring to (or what happens when you try to watch the videos) it's impossible to give a definite answer.
However most video sites rely upon Flash Player functioning properly on your computer. It frequently doesn't. Go to YouTube and try watching any video. If you can't, it's a Flash Player problem.
Solution:
Uninstall Flash Player from your computer. (It's probably listed as 'Adobe Flash Player Plugin'). Then reinstall it from here:
http://get.adobe.com/flashplayer/
Chris