No, I wasn't dreaming...the edges of the screen were undulating gently, in and out, as if they were the waves of a calm sea.

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Sounds like some of the capacitors on the analogue board are failing. A similar scenario occurred with my 512ke/Plus hybrid where I switched it on, the screen was bouncing back and forth, and upon restarting the computer, a bright vertical line appeared. Quite scary come to think of it, but such is life with older electronics.