Thanks for your advice.
Actually this is an AMD A8-3850 processor with an integrated Radeon graphics processor. So there is no discrete graphics card or, indeed, even one integrated into the Motherboard. Of course the Motherboard does supply the necessary connections to route the video to the CPU.
I am leaning towards the motherboard being an issue - but really have nothing definitive. The maximum resolution on the PC video is 1920x1080 @ 60Hz which is what it is set to under Windows. Under the BIOS, I cannot say what the resolution is.
The Vizio TV that it is experiencing issues with is a 1080p 120Hz TV.
I have also tested it against my 720p Sanyo Z3 Projector (unknown refresh rate) and an Element 19" 720p 60hz TV. I seem to only be experiencing these problems with the Vizio.
I can't see this being a resolution/refresh issue for two reasons. 1) The issue only lasts for a short period of time and 2) This isn't the scrolling type of flicker that refresh rates tend to cause. This is a more of a random jagged line flicker. I have posted a video I just took here
(comments on video). Unfortunately I was able to only catch a minor occurrence of the problem not one of the lengthier fits where the whole screen goes kind of bonkers.
I also think that a bad cable wouldn't exhibit only this temporary behavior. As I mention it only lasts for 20-120 seconds and also only if the TV has been off a while. I did purchase relatively cheap cables (online deal and some from Frys) but they are rated high-speed and they seem to work fine with everything else.
It's frustrating since I can't recreate this issue with a different combination on either end. I have more tests with the computer going into multiple inputs (and will have one more tomorrow) but have a limited number of HDMI input sources