Macbook Pro won't boot-up

To me it almost sounds like the graphics processing unit/logic board has failed.

You could try performing a Parameter RAM (or "PRAM") reset along with an System Management Controller (or "SMC") reset to see if the situation changes, however by your description I doubt it'll make a difference.

To reset the parameter RAM settings:

1. Turn your computer off.
2. Turn the computer back on.
3. Immediately hold down Command-Option-P-R until you hear the computer chime twice, then release the keys.

To reset the System Management Controller on your computer (which has a removable battery):

1. Shut down the computer.
2. Disconnect the MagSafe power adapter from the computer, if it's connected.
3. Remove the battery.
4. Press and hold the power button for 5 seconds.
5. Release the power button.
6. Reconnect the battery and MagSafe power adapter.
7. Press the power button to turn on the computer.

Failing that, I'd recommend taking the computer into an Apple Store or contacting AppleCare to arrange for repair.

Usually, they won't outright replace a computer unless there have been several failed repair attempts or it's more economical for them to do so. However, you could always suggest the idea to them based on the failure of the logic board and the LCD screen and see what they have to say, there's no harm done in doing so.

Best of luck and have a great day.

 

Troubleshooting: My computer won't turn on

 

If it's the logic board and it's still under warranty Apple will replace that part, not the machine. After 4 parts have failed while still in warranty then they will replace the machine.

Best thing is to take it straight to an Apple store, they'll sort it out within a day or 2.

 

The LCD, wireless card and logic board would qualify but the battery and charger don't unforutantly, battery being a naturally degrading object and the charger being separate all together.

To be fair the guys in the apple stores are very understanding so mention it, you never know!