What player are you using? Quicktime? There a couple of things that come to mind: (not really in order) first, check what video format are you using on the videos that you have already saved on your hard drive. Second, update the Adobe Flash player and make sure you have Javascript enabled. Third, if using Safari, check the Website tab (under Safari preferences) and make sure you don't have the websites blocked from certain features. Fourth, you may need to check any Safari extensions that you may have added in the past.
Let me know what happens and if I can help some more.