If the blue lines are on the entire screen, and not just the video portion of it, it could be something called "chip creep" - when heating up and cooling down causes the components inside the laptop to expand and contract accordingly, and some of the boards wiggle out of their slots on the motherboard. This happens more on laptops because everything is so snug together.

I posted that because I hadn't read it yet. If it's just the video portion, then you've been given lots of great advice thus far. I'm A+ and Net+ certified, so I'll do what I can to help.