The real issue is with the display hardware; presumably there's a loose connector somewhere between the video adapter and the LCD panel, which may explain for the banding. Or a possible frayed-out video wire.
As most repair shops tend to charge much for a laptop fix, the solution (at least for diagnostics) is to get an official HP servicing manual (you can Google for them; they're mostly in PDF format), prepare the appropriate tools and take the laptop apart (did just that with an older Compaq and a more recent Acer, both with heat problems but resolved successfully) until you check if the connector in question is the culprit.
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