General :: Retrieve SMS Database From Dead Galaxy Nexus

My GNex took a baseball to the screen; the screen is shattered and unresponsive, but the phone will power on and I can see the file structure if I connect via USB to my PC. I've retrieved all the files and photos that I want to save from the phone by copying to the PC, but not the text messages. I had a backup for the text messages, but it's gone (different story for another time). So I've been searching for a way to retrieve these text messages that can be executed entirely from the PC side, since I have no way of installing an app on the phone. I'd either like to be able to copy the SMS database to a new phone via PC, or dump it into some sort of manageable text format.

From the searches I've done, it seems like I might be able to do this using some sort of developer's code; (i.e., Install this program, plug in the phone, enter these lines of code, etc.)

The phone is stock (not rooted), and was just recently updated to ICS 4.0.4 (?)

Samsung says they can "fix" the phone for $160+, but that they won't be able to save any of the data since the phone isn't navigable (I assume they'll just send a replacement).