NVidia does support multi-display, but configuration will be a pain if (up to three) monitors aren't identical resolutions.
Also, you're basically pushing 4K worth of pixels from a single GTX 680. It's just not quite macho enough when tasked with heavy video playback/decoding or peak 3D render/physics sorts of stuff at that combined resolution.
If you're only running 4GB or 8GB of main RAM then things will bottleneck whenever 4K worth of texture data needs to be shuffled to and from the 2GB VRAM on your GPU. The GPU frame buffer needs to cache data in main RAM whenever it isn't large enough to hold everything it needs - not enough RAM can mean slowdowns and stutters (especially if it needs to extend a virtual cache to much slower NVRAM SSD storage or horribly glacial magnetic HDD storage).
You can try running all your RAM (both the good and bad sticks) at a lower JEDEC, say DDR3-1333 or DDR3-1600. If your bad stick still fails at slowest compatible speed then just toss it (but keep the heatspreader, if you like). Maybe try it in another mobo first. Maybe try using an electrical contact cleaner on it first. You've already done everything else I would recommend, aside perhaps from a clean OS and driver reinstall.
The GTX 970 should have been a mighty upgrade. But what you really need is more RAM. I would purchase a DIMM pair
identical to your existing (4GB or 8GB?) working one, or even remove all your existing memory and upgrade to a 4x4GB DDR3 kit. You may still see better performance when driving your second monitor from the integrated GPU.
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