Something else I forgot to mention; Adobe Flash hasn't 'officially' supported Windows 2000 for some time now. Here's a link to an older version of Flash that should *still* work with Youtube.
1. Extract the folder to your desktop or somewhere convenient.
2. Double-click on fp_10.3.183.11_archive
3. Double-click the 10_3r183_11 folder
4. Here's where some guess work might be needed: First, try double clicking on "flashplayer10_3r183_11_win.exe". After the setup has completed, restart your browser and try running a Youtube vid. If it doesn't work, try these other files:
Let me know if this works.