excalibe and Trilvester's problems don't seem to be the same. I'd say Trilvester's problem is most likely to be a dead battery. If your 10v is new, get in touch with Dell and get it replaced.
excalibe, it sounds more like yours is something to do with the screen power. Because it only occurs when it's running on battery power, it's unlikely to be anything to do with your AC adaptor, country or voltage. It could be a fault with the power supply to the screen backlight or it may be a software problem. Does it happen on all screen brightnesses or, for example, only on one or two? In other words, does changing the screen brightness make any difference?