You can contact Apple and see if they will still honor this program. It right at its end:
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iMac (27-inch): AMD Radeon 6970M Video Card Replacement Program
https://support.apple.com/en-us/HT203787
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If not come back and we'll see what you can do. It's crashing right where it loads the video software. To confirm try hooking it up to an external monitor and try booting in Safe Mode (hold down Shift key on start up).