How do you fix an LCD that become black in one half after a few hours of use?

There's a couple of things that generally will cause that to happen. Since you didn't specify what type of device it is such as a computer display or a LCD television, I can't really be too specific.

The first cause may be that the connections to the lower half of the LCD panel have become loose. Since most connections to the panel itself are put into place by an adhesive, chances are that the connector has lifted' from the circuit board and all it needs, it to be pasted back down.

The second cause may be that one of the display driver chips have gone bad. This happens more often in LCD TV's, and since this isn't really a consumer repairable item, the whole driver card is generally replaced.