As much as I've heard about copyright issue:
I hope I'm not lying...
Even when not for profit - as soon as there are more than 1 or 2 copies for personal use (or backup) you are in violation of the copyright (for example, including music (or other files) in webpages or making them available to others (per FTP or downloading) constitutes (re-)publishing/broadcasting of this music to the public).
You can use most
clips (short part of the original) without license cost or royalties by displaying a proper notice where the clip was taken from.
So if you are going to publish the video to more than 1 or 2 people, it's illegal to use copyrighted music in it.
PS. Besides clips, there are some works you can use
without needing a license:
- the term of copyright for the work has expired;
- the author failed to satisfy formalities to perfect the copyright;
- the work is a work of the U.S. Government;
- copyright licensed MIDI music files