University of Maryland has a great web page on copyright law in the US: http://www.umuc.edu/library/copy.shtml#internet
The best rule of thumb regarding copyrighted material is: don't use it
In the 90's when hip hop artists were sampling music from past decades there was a big debacle from the original musicians suing the hiphop artists for borrowing only parts of their music, like a drum beat, guitar solo, or vocal track. DJs still sample in clubs, but it's generally frowned upon and potentially expensive to borrow parts of copyrighted material and distribute it or attempt to sell it.
It's the author or owner's right to distribute, rewrite, and perform the work. Given the methods of filmfights to promote its filmmakers, it could be construed as a form of distribution if your film contains copyrighted material. So if a work contains music from a copyrighted source, it could be a form of copyright infringement.
Unless you have the express permission and signed or confirmed lease and license for that work, which in some cases you can obtain by contacting the owners. A year or so ago Moby was giving free licenses for some of his music for aspiring filmmakers to use in their films.... check out mobygratis.com. Make sure to follow the legal representation's advisement on how to credit the music that you use - some licences require certain stipulations. If you are using music that a friend or acquaintance composed, for legal purposes it's a good idea to get in the habit of getting your composer to sign a recording agreement or release. PDFs of these documents can be found on the web (try google).