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Did you re-use the battery from the first phone in the second phone? if so, a battery defect could cause what you describe, perhaps. But it sounds as if you haven't.
Were both phones of the same model line? (If so, it may be a badly made model line.)
Were both phones purchased at the same store or through the same vendor, or is this second phone a warranty-swap/exchange for the first? (If so, the vendor may have passed off poorly made phones to you... or, if the two phones were not sold shrink-wrapped in their packaging, they may both have been culls or otherwise defective phones not at all in new condition, etc.)
The way it sounds, you might have a loose video cable in one, and a defective LCD touch-screen unit in the other... resulting in the same look, though from a different problem. I really don't think it's your fault, unless you dropped it, got it very hot, allowed it to drop below freezing temperature at any time since you bought it, or got it wet, etc.