If the backlight is still on (ie - screen lit up) it's not the inverter, especially if it's an LED screen that doesn't have one
It's either the panel itself or the ribbon cable that connects the screen to the motherboard, the panels are roughly £35 and cable's around £10-15 from ebay. If the screen corruption changes as you open/close the lid chances are it's the cable, otherwise its the panel.
If you post a picture of the laptop or the model number I can give you an idea how easy they are to take apart, I do loads at work.