Try troubleshooting the Safari .plist file.
Quit Safari. Open a Finder window. Select your Home Folder in the Sidebar on the left. It has a small house icon. Then open the Library folder then the Preferences folder. Move the com.apple.Safari.plist file from the Preferences folder to the Desktop. Relaunch Safari. Try a video in a new tab. If that didn't help, most the .plist file back to the Preferences folder.
If that didn't help, check Safari / Preferences then select the Extensions tab. If you have any installed, turn that off, quit then relaunch Safari to test a video.