Re: Lines, Black and white, sometimes color?!
The overheating thing is a good thing to check as mentioned before.
Another thing that might be possible to try is - if they are built anything like Dell laptops, beneath the keyboard, there will be a ribbon cable attaching the LCD to the motherboard, and often it can come loose and just needs to be re-seated.
On the Dell laptops, the plastic bezel above the keyboard pops off, then you need to remove a few screws for the keyboard, fold the keyboard up, and the cable should just be right there.
Might be worth a check. See if you can get the lines to appear on an external monitor as well - if they do appear on an external monitor, it may isolate the issue to your video card specifically.