Hi there predjee.
The k-lite codec pack (or any other codec pack for that matter) doesn't help you with any browser issues.
Those videos (like the ones you'd find on youTube etc) usually require flashplayer ( i.e. Browser plugins).
Normally upon opening such a video the browser would notify you about any missing plugin and offer a download link. You could check under Tools/Manage Addons if that plugin is disabled by any chance.
-DG
Another reason for videos not playing could be disabled/blocked Javascript for that specific site (i.e the Noscript plugin for Firefox)