|Since your external monitor works fine, then there is nothing wrong with your video and the majority of the laptop pieces.|
Problems of not being able to get enough brightness or an always black screen on a laptop display are usually due to a defective or dead backlight (CCFL) or voltage invertor that supplies high voltage to it, but according to info I found on the Samsung site, lines of white or of one color across the screen or always black lines or patches of black or a lot more black pixels than you may have had before indicate the LCD assembly or the wiring to it is damaged. If fixing damaged wiring, if there is any, between the laptop base and the LCD assembly in the lid does not cure the problem, the whole LCD assembly in the lid needs to be replaced.
If the assembly needs to be replaced, sometimes you can find a refurbished assembly especially if your laptop model is a little older (e.g. for $150) or you may only be able to find a new assembly (e.g. for $250). You can replace it yourself if you're handy and have or can get a Maintenace manual for your model, but if you're not you'll also have to fork out the labour charges to have someone repair it for you.