Some pixels stay black?
Those are called dead pixels. It can, and often, happen with any LCD monitors.
It's not possible to correct them without completely replacing the panel.
If there are only a few non-adjacent, you usually have to live with it.
If they are clumped together, it's often possible to get a replacement if it's still new and under warranty.
howtomendit.com for free repair help, information and advice.
Try fixfault.com to fix notebooks/laptop pcs.