To update my experience:
I was able to boot up from a clean install and also after migrating applications and data.
However, I did not migrate the computer settings.
I still see some strange things occurring but this may be due to Spotlight or some other issue I can't yet explain.
I don't have any random log outs and the system is definitely more quite with the GT 120.
However, swapping out my ATI 2600 and replacing it with my GT 120 did not help.
The brick drive is still bricked.
I am working with Apple customer support to try and help them figure this out.
I suspect some antivirus software I had installed previously that added a kernel extension (Kext) that will not let me reboot into the bricked drive.
I say this because the migration over to a clean drive would not have brought over the kernel extension.
I am guessing they will probably be able to point to something I did wrong or some software kernel extension I added.
If you are planning on doing a clean install, get a backup first to another hard drive using Superduper or carbon copy.