If you have warranty taki it back to the shop. If you want it fixed take it to the shop and ask them for a offer to fix it. If you can fix it yourself, find the screen type and buy one, you might find one on ebay or through sony. If it's a cheaper/older laptop, it might not be worth fixing.
edit: If you a have monitor laying around you can hook it up to the laptop and use it as a desktop computer.