If I remember correctly, direct Youtube playback doesn't work in VLC versions that ancient. I remember testing the last release working on Panther and finding that functionality missing, so I guess it won't work in Jaguar.
If I am wrong than the issue is the lack of an updated lua script in /Applications/VLC.app/Contents/MacOS/share/lua/playlist/youtube.luac
Download the latest version of VLC (at the moment 2.0.8) copy the corresponding youtube.luac file (you will have to right click on VLC icon, choose "Show package content", than navigate to /Contents/MacOS/share/lua/playlist) and paste it in your VLC installation at the path I gave a few lines above.
I have no idea what other options you have in 10.2.8, but try this bookmarklet:
http://marklets.com/PwnYouTube.aspx
If it works in your browser (big if, considering the lack of modern browsers in Jaguar) it will give you download links to the video files embedded in the Youtube page you are visiting. Copy one and open it in VLC. You should be able to get video playback.
If this doesn't work you could try getting the links from one of the many websites for Youtube downloads (but beware of the ones requiring Java).
Good luck, and let us know if this worked for you.
PS: just for curiosity, what browser are you using in 10.2.8?