Hello,
did the laptop previously get really hot and shutdown or reboot on its own?
did you install anything prior to this problem? Did you drop the laptop?
Typically, while booting, the GPU uses very low resolution, I can't think of a reason why it would be off center though.
Same behavior in windows as in your whole desktop appears to be slightly higher? or some programs launch above taskbar?
also, vertical lines on screen could mean a few things, it could be the screen failing or the video card being damaged in some way. To double check if it's your screen or GPU connect an external screen, if the same thing happens on external screen, it's the GPU/motherboard if the external screen is fine, it might be just the screen of your laptop that needs fixing.
Hope that helps.
If you could post a picture of what the boot screen looks like that could help visualize what you're looking at.
(you can use websites like imageshack.us or photobucket.com to unload the picture and then copy the link into your forum reply)