How much it costs will depend on which component was damaged. Keep in mind that you may notice other issues later on once corrosion sets in on the electronic components. A backlight issue could be due to the Display Assembly (light sensor), Top Case/Keyboard Assembly, and/or the Logic Board. All three of these components are expensive ($300+US just for each part).
Since the damage is already done and the rest of the laptop appears to be working, then you can just use it as is until more issues develop. Otherwise you will need to have Apple or an Apple Authorized Service Provider to examine the laptop and provide you with a repair estimate.