Display does not power on but external display works

Since you have already confirmed that it works with an external monitor. You know the video chip is good. Now boot your laptop, without the external monitor and take a flashlight, pointing it at the screen, look to see if there are faint images on the screen such as items on your desk top. After that, while it is still booted, move the screen back and forth through its natural range. Does the LCD's backlight even flash on - off when doing this? Please let us know the results of both of these.

Please tell us about your power management settings. If you don't have it set up to go to sleep, but only turn off the monitor when the lid is shut it could be the laptop thinks the lid is shut.

The a1286 has a LED backlight. They have no inverter board. Has this laptop been exposed to liquid, even a small spill? What are the last 3 characters of your serial number so we can identify the exact machine and better be able to help you?