Often the laptop's screen will need to be replaced, but it is a good idea to check the connection first, because a loose display connection can cause problems too.
Your laptop's screen is connected to the motherboard and you can usually see the connection if you remove the laptop's keyboard. Check your manufacturers website for instructions, but it usually isn't too difficult to remove a keyboard, although you must be careful not to damage the keys.
If it is the display, you can often find a good deal on ebay and it would certainly be cheaper than buying a new laptop.
Your laptops service manual should have a section on replacing the screen as well and there are usually some good guides online with pictures.