Can I use the videos marked as "youtube standard license" for a non profit video?
I know you probably already found this link, but according to Yahoo, you will want to contact the Uploader before you try to use it. Thats what I would try. I don't think I would want my youtube videos just used by anyone who wanted to. Seems this person ran into that problem.

If a video is only using the Creative Commons License you may use it, but otherwise contact the YouTube user before you use it.

Good luck.