My daughter did a video for a High School class project. She used a partial soundtrack from Wizard of Oz I believe and posted it on youtube...I went back a little later to watch it and get a niotice that it had been removed at the request of the copyright owners...
It all depends on how draconian the copyright owners are. I'd take the melody of the music, run it through a sound mixer (hand type it if you have to) change a little here and there, and it is a new music piece, yours to own, even if it is based on somebody else's work. Not entirely kosher, but that is how the copyright law is written, only the work, in its original form is protected. Takes more work, but it saves headaches down the road.