I am guessing that your video card's D/A converter has probably started to die.
Does your video card have a DVI output? If so, can you try using that to connect to your new flat panel?
Another option or two is that either the power is _really_ dirty coming in to your system making the D/A converter behave weirdly (or making the display drive itself strangely). A altogether different option is that there is some massive amount of interference around your video cable that is degrading the signal. So another thing to try is moving your computer to a different place in the house and only plugging in the bare essentials.
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