No, music not original to you is protected by copyright. If you post this work to the web you are infringing on the owner's rights. A possible source of original music is MySpace and other web communities.
Many artists post their music hoping to be discovered and looking for opportunities to get exposure. You must get written consent from the artist in order to use their work and credit the work in your piece.
You can also compose your own original background music using a simple consumer-level program, such as Garageband. By dragging and dropping music loops provided by the program, you can create different styles and genre of music based on the rhythms, instruments and beats you choose. It is simple, intuitive and you do not need to be a musician.