I'd have to agree and try the kapton tape but it's not a guaranteed fix. Ultimately these are all great suggestions but in reality you have an almost new Macbook. If you ever need any kind of warranty service on the computer you are going to have a tough time. You are looking at $749 for the part alone. If it in in fact the logic board.
My guess is that the laser diode for burning/reading DVDs has failed or is out of calibration. I see this all the time. I would say it's not related to the formatting of the drive. The replacement drives are cheap and very easy to replace.
If you hold down command + option then launch iPhoto. I'd check off all the boxes and see if it can repair it self. It will take some time but I've seen good results. Also as machead3 said check your free hard drive space.
Did you use any of the delocalizer programs that are available? You might have removed the language packs. I'd try an archive and install using the original OS disk. Once that is complete, re-apply the updates. Once you're satisfied everything is working, you'll need to re-add any printers and delete the Previous Systems folder in the root of the hard drive.
The problem is it's a line of dead pixels. The only way to resolve it is to have the screen replaced. Some people have tried apps that flash random colors and they claim if you have leave it running long enough it will fix it. My years of experience tell me otherwise.