Firstly I assume it is your home PC, and not a locked work unit. If you go to Adobe's main site and download the flashplayer suitable for your Windows version, and your browser.
They have specific versions for Internet Explorer or other browsers such as Firefox, Opera etc. Also 32 bit and 64bit versions. Get it from this page and select the appropraite versions. :- http://get.adobe.com/flashplayer/otherversions/
If the instructions above don't resolve the issue, please also try the following:
Temporarily disable pop-up blocking software installed on your computer, to test.
Allow youtube.com?hl=en_GB as a trusted site in your Firewall software.
Ensure that other applications such as QuickTime, iTunes, Real Player or Windows Media Player aren't set as the default streaming application, as this might affect the video player.