Green moving pixels is caused by a bad connection somewhere or a faulty component on the video card.
1) Line noise.
If your HDMI cable has a bad wire inside, perhaps on the ground line in the shielding, this can cause twinkles.
2) A loose connector.
This can be on the video card its self due to a cold solder joints on the address lines somewhere, or the connector on the HDMI cable.
3) A bad component on the video card.
A bad chip or capacitor on that particular port interface can have an open or be out of spec. As the temperatures change, this can cause things to happen, or in some cases happen right away.
4) A short...
A rare thing, but it can happen from a bad cable, dirt or garbage in the connector, or on the video card.
Before you panic, I would replace the cable. The issue can be as simple as a faulty, cable causing an open or a short. This is the cheapest and easiest thing to try before looking elsewhere.
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This problem brings back some memories for me! Way back, and I mean way back in the mid-1980s (I'm old), I used to repair video terminals. On one particular model, there was an array of buffer chips to output the data on to the screen. We had some terminals that had a problem with blinking stripes and dots on them. The problem was traced back, by me actually (pats self on back), to the output buffer circuit that was driven by a crystal oscillator and a flip-flop (74F74) chip. What was interesting is the problem went away if the chip was changed, which meant the circuit was out of spec, or marginally out of spec, and the problem also went away if the oscilloscope probe was placed on the buffer chip clock input. These chips were parallel shift-register buffer chips (74F266), that would clock the data through them and out through the video-controller circuit. Since the problem was with the clock circuit, it was resolved by placing a very small 15 pf (pico-Farad) capacitor on the clock input on the 74F266.
Thanks for sparking a memory in a weird way!