O.k. we got the song figured out, thanks to this thread. Now I need to figure out who I have to talk to in order to: get permission/pay to the order of so I can use this song in a commercial… Any ideas?
You first need to determine whether the copyright is still in force. If not, you need do nothing (see next para., however). If so, you will probably need a lawyer, since even if you are able to get permission to use it in a commercial, you will most certainly have to pay for it and have the customary convoluted contract that requires lawyers to negotiate and write. A lawyer that specializes in this stuff will know who to contact and what to do.
Next, are you going to make your own recording, or use an existing one? For an existing one you will have to go through the same rigamarole with the artist (or rather, the artist’s lawyers). Probably cheaper and easier to hire a few studio musicians to whip up a version.
Here a link to the Harr Fox Agency, which handles song licensing. There’s a pdf file on that page and instructions on where to send it.
(I’m not affiliated with that agency, and don’t know how they compare to other agencies that negotiate licenses. Caveat Emptor.)
Simple: ASCAP. They handle any broadcast use of a song. This page gives contact e-mail addresses.
Sweet! All the stuff I found online was about if you were an artist and wanted to license out your songs 
** RealityChuck** nailed it, nice post.
This ASCAP link tells you more detail about this specific song.
You don’t necessarily need a lawyer, if you’re confident about what you can negotiate and feel comfortable with reading licenses.
ASCAP/BMI/Muzak is good if you just want a rebroadcast license. What you’re doing will probably required a mechanical license, which ASCAP won’t do. You’ll have to hunt down the copyright owner (typically record company or artist) and ask them for permission. As another poster mentioned above, Harry Fox is a good place to start.
If you can remake the song w/ studio musicians (or yourself), however, you can get a compulsory license. It’s usually much cheaper (I believe the amount is set by statute) though the effect is not always as effective, depending on how you want to go about placing the song in the commercial (just the song, or implying that the artist is somehow associated with you/your product). And depending on your commercial, the copyright owner (assuming that the song is still protected, of course) may/may not cut you a deal. (For example, if your commercial is for a non-profit cause, the owner may cut you a better break than if you are Cocca-Cola.)
Good luck.
Ah. I hadn’t realized you were interested in a Gershwin song. Then you should probably contact http://www.gershwin.com
Though since Gershwin helped found ASCAP, they can probably also point you in the right direction.