The US copyright law provides (or provided, the last time I looked it up) for what is called a "mandatory mechanical license," with regard to any song that has ever been recorded and released publicly, by anyone. In other words, you have to ask permission, but the owner of the copyright has to give it to you, if you pay. There is a statutory royalty of about 7 cents US, per copy of the song distributed on records. That's _distributed_, not sold. You have to pay on the ones you send out as promo material or give Aunt Zelda for Christmas, not just the ones you sell for $$$$.

Harry Fox Agency, the great villain in this long thread that's been running, is also the US clearing house for these licenses, so you go to them if all else fails. It's probably better to go to the composer directly if you have a contact address. He/She/It would presumeably rather license the song directly and get the whole royalty themselves, than give HFA a chunk for handling it for them.