Time to go deep and clean the internals of the laptop. Be sure to test if that helps. If not I replace the heatsink compound, cleaning as I go. Lots of youtubes on this common work.
I've got a HP Pavilion G7 laptop, that the screen will start to get lines on it, and then get really jumpy, and then eventually will freeze up with whatever was onscreen with all the lines and missing areas. I replaced the thermal material on the integrated GPU and now it works a little longer before it acts up, but when I connect it to an external monitor, the monitor picture is perfect, and the laptop display is still messed up. Is it the LCD or is it the graphics processor? I want to know before I get a new LCD and find it still doesn't work. Thanks