If you go to the m.youtube.com mobile site instead of the desktop site you may have better luck. While the desktop version runs on the iPad in Safari, it has some quirks, and will not filter out the older Flash based videos.
The mobile version is considerably less capable, but it is easy to use and only serves HTML 5 video.
And then there is the YouTube app. Since YouTube improved the mobile site it is the least capable way of viewing movies, but it should work.
If for some reason your server is blocking any of these, then you would have to talk to who ever is managing it to make sure they are not blocking the site on purpose. Strange if they are, but you never know.