I have tried to install different drivers for the cards, and I have tried installing a previous version that supports both cards. Neither worked. It seems to be the combination of the new card and anything but the new driver that makes GUIMiner not start.
Now, when I am running only the new card, Phoenix and Stratum Proxy, it stopped working tonight, a few hours after I started it. I restarted the miner this morning and it worked again. I hope it's a one time occurance, but I doubt it. It didn't happen with Phoenix and BCPool. Any guesses?
This happened to me when I upgraded Catalyst from 3.1 to 3.4 using only a single card (7770). Catalyst 3.4 fixed some display problems (flickering pixels) but slowed my miner around 20%. I wanted to revert back to 3.1 so I uninstalled all AMD software (including the driver via device manager) and then installed Catalyst 3.1. GUIMiner failed to start after this with no error message.
I can only speculate, but I believe that the OpenCL package is not removed when Catalyst is uninstalled. Software developers frequently leave support packages, such as OpenCL in place because they cannot determine if other software not written by them may be using the interface.
So when the older reinstalled Catalyst 3.1 attempts to use the newer OpenCL from Catalyst 3.4, its probably misusing a changed interface causing an error that GUIMiner doesn't know how to handle.