Two possibilities:
1. The LCD connector isn't making good contact.
2. The driver circuit is faulty.
If it's 1 and you are confident about opening the device, the connector will be a 'zebra strip', a plastic strip made from hundreds of layers, alternating between conductive and insulating plastic. You can see where it contacts the glass of the LCD beneath the display. There will be a similar line of circuit board connections behind the LCD and the zebra strip links them together. It has to be under slight compression to ensure good contact but sometimes if the device is dropped, it shifts for a moment and dust gets underneath it. The dust holds the conductive plastic way from the glass givng a bad connection. They can usually be repaired but you need to be extemely careful and dextrous. Wipe the circuit board, LCD and zebra strip with lint free cotton cloth and NEVER use a solvent. The connections on the LCD glass are so thin you can see straight through them so anything even remotely abrasive will simply wipe them out of existence!
If the problem is 2, your only option is to replace the LCD module completely - if you can get one! They are usually custom made and only available from the device manufacturer. You could be lucky and find they used a generic display but even they can be difficult to source in exactly the right size to fit back in place.
Brian.