Short answer: No!
Long answer: It's illegal to use copyright protected music for any purpose what-so-ever, profit or non-profit. That said, if you don't show anybody, nobody will ever know, so you can do what you like. But i'm assuming you don't want to do that and you'll upload to YouTube or the like, in which case this is illegal and against YouTube rules. However, are the major studios going to be too bothered about you and your little vidoe? Probably not. The worst that will happen is YouTube will remove it.
Better to play it safe though. Go find some original music for your movie, there's plenty of people out there willing to offer that to you.