Please tell us if the "screen" is a laptop screen or a traditional tube-type monitor. If it's the later, connect it to another computer and see if it exhibits the same sysmptoms. If so, the internal circuitry of the monitor is probably failing.
DMR
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The exact symptom you described is usually a result of failing beam-drive electronics in the monitor, but if it doesn't happen when connected to other computers, then that diagnosis does become less likely.
Have you been able to connect another monitor to the computer in question? That would be the next obvious test.
DMR
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