If the CPU had so much corruption that the video card would work, but show garbage, then I doubt the CPU would work. On the other hand, corrupt memory would cause a video card to show nonsense. The memory I am thinking of is not the RAM, but instead the BIOS and firmware used for PCIe. Odds go to the motherboard compared to the CPU.
There is also a possibility of inadequate voltage from the power supply to the video card. Once again, I'd think odds are towards the motherboard instead of the power supply since there are regulator and other components on the motherboard passing to the PCIe slots.
It's a guessing game if you can't swap those out one at a time. FYI, if you were to get a new motherboard, but the socket stays the same and the CPU stays the same, then your existing Windows license will stay valid (you might have to jump through some hoops so to speak). If you change the CPU (or the socket type of the motherboard) you'll end up needing a new Windows license.