In Safe Mode, I would probably want to uninstall the descreet video card in the device manager. When you do that, you should have an option to remove all the drivers also.
Then I would uninstall the onboard graphics and its drivers. Since you have the same brand of video manufacturer, there are probably files in common for both devices.
If you don't have the latest drivers for whichever video source you will end up using, you should be able to download them and have them ready. Seems like the AMD video cards have two areas of drivers, and one is a Catalyst. I don't have any experience with that type so you will have to be the best judge.
If you need to set something in the bios for onboard or discreet video, do that prior to reloading the drivers. New systems may have something that shares onboard and discreet video, so perhaps make sure that is not functioning for now.
Try to load your most update to date drivers, since Windows will try. But if you can't, just make sure you do get yours loaded.
I don't know anything about the compatibility of the cards you are using and Windows 7, but you might keep it in mind in case you need to upgrade the discreet card.