All the above advice is good, but you have to remember to very clearly state what you'll be doing with the music. For instance, music in an autodesk animation is quite likely to be performed in front of a large-ish audience at a regional. And if it wins, FIRST will want to copy your animation and redistribute it to teams next year. These uses aren't necessarily implied in "We want to use your music for an animation our club is making" and their much more likely to be refused. FIRST redistributing animations is the primary reason they don't want you using copyrighted music, since it's difficult to get a band to agree to that kind of license, and FIRST would have to keep a record of the license, etc, etc.
Now, copyleft music is a different matter. There's a fair amount of music under Creative Commons licenses available on
Jamendo. Anything that says NoDerivs won't work, and anything that says ShareAlike means you have to license your own work under the same license as the music... But any other license on there would be fine.