Here's a link that might help. If they don't have the track you're interested in call ASCAP or BMI (or whatever performance rights org is on the label) and ask them. You can make this happen, but it can take a while as often many people are involved in the decision (record company, producer, songwriter, performers, etc.).
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Unless your DVD is exempt for educational purposes (and I've no idea if that's even possible, but you can distribute music for teaching purposes under certain circumstances) I don't recommend even pursuing this - it's a long winded and expensive process, which is why broadcasters have blanket agreements for licensing. You have to contact the record label for the artist directly, and most of the time you won't like the answer.
Have a look at a halfway option, Pumpaudio, where you can license music, some from actual artists with lyrics, or royalty free sites like shockwave sound.
Whatever you do, don't hand a client ANYTHING without licensing in place.
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The company I work for once used one of the larger stock image libraries to do the rights search and negotiate for us. As others have pointed out, the process isn't cheap. There was an up-front charge, and you pay it regardless of whether or not you can secure the rights.
All involved parties (record label, recording group, composers and publisher) must be contacted and come to an agreement to license the material, and many times those parties have to be negotiated with individually. Some or all of the parties involved might also have a most-favored-nation clause, which can drive up the cost pretty quickly.
And did I mention, the band doesn't take American Express? It wasn't quite as bad as a request for cash, in small, unmarked bills, but it was close with a ridiculously short turnaround.
Be prepared for a five-to-six figure quote for the music, depending on usage.
In the end, a great learning experience.
As this was several years ago, the situation might have changed. And if the performer is media savvy (think Moby), you might luck out.