Sounds like a potentially critical hardware failure. Reading your post you state that it starts off ok and then you start to get lines that appear and I am guessing it gets worse to the point that the display is not legible.
I have seen three causes for this ( all hardware related ):
1.) GPU is bad - for the video, and when the system boots and the GPU Graphics Processing Unit warms and it starts to get progressively worse with no lines or blocks, then a few and then many. ( This is a critical failure and the laptop at this point is toast if the GPU is shot. )
2.) Bad Ram - Laptops usually share a portion of Ram from system Ram, and a bad Ram stick is causing the GPU to render improperly. If the laptop has an extra Ram stick in it paired with another stick. Remove one of them and try to boot the system from each stick individually to see if one stick causes the problems and the other to work fine. If it works out this way you now know your solution ( throw away the bad stick or replace it.)
3.) Bad LCD display - Easiest way to tell if the display or the GPU is the cause is to plug in a VGA monitor to the auxilary VGA port if available to see if although the laptops display is full of lines, the external VGA display shows perfectly fine and the computer runs fine. ( LCD displays can be replaced, but on a 5 year old system, it would be better to leave that external VGA display plugged into that laptop and use it as a desktop for the remaining life of that laptop than to spend over $300 to replace the LCD display. ( If hardware savvy you could try to find a same laptop on ebay etc with a good display and mix guts to make one good unit for less money. But it is a lot of precision work and patience with precision screwdrivers.)
