Finally some answers...

I've been, on occasion, scouring the net for answers on my AMD hardware on Ubuntu.  Support has been incredibly awful but I wasn't surprised.

lspci describes my hardware as: Advanced Micro Devices [AMD] nee ATI Thames XT/GL [Radeon HD 7600M Series]

This provided me with an interesting article that seems to explain a possible solution to this problem.  Essentially, it looks like you need to install the latest beta driver from AMD to get things pseudo working.  Specifically, the post mentions that the 13.2 Beta 3 version works on the laptop.  Ubuntu distributes the 12.6 Catalyst which is virtually unusable here.

One has to wonder when Ubuntu plans to put the aforementioned driver in the repository.

Update:
An additional article that discusses this on Ubuntu.

Here is the launchpad link for Ubuntu's fglrx stuff.