OK first, you need to make sure you are having the same problem I was experiencing. On my Samsung 11.6" ARM Chromebook I was having a problem that whenever I turned my Chromebook on it wasn't turning on the backlight on my screen. You can tell if this is happening by shining a light onto the screen. If this is what is happening to your chromebook the light will allow you to see that there is a very very faint image of the normal login screen. You can also do a reset on it to get it to come on (To do a reset press and hold the power button for 30 or so seconds, then let go and then press the power button again), but it will keep doing it until you follow these steps each time the Chromebook is turned off.
1. first make sure anything you have saved on your chromebook that you want to keep is saved to a thumbdrive or external hard drive, or to your google drive. We will be turning developer mode on, and doing this will wipe the 16 GB SSD drive on your chromebook and reset it to factory settings (no user profiles,etc.)
2. next power off your chromebook using the reset method described above (otherwise recovery will show up with the same issue where the backlight is turned off).
3. press and hold the esc and the refresh key (the one that looks like a arrow going in a circle), and then tap the power button. this boots the Chromebook into recovery mode.
4. you are now in recovery mode, the next step is to press control-d and you will then it will ask you to confirm that you are about to go into developer mode once you have confirmed the system will reboot into dev mode and show a progress bar across the top. once this finishes it will reboot again and take you back to a screen where you are prompted to press space to exit developer mode.
5. Press space and the system will erase the storage on your chromebook again and then reboot to normal mode.
If you wish to keep the Chromebook in developer mode you can press control-d and then skip step 5, however you will have to do this each time the Chromebook is turned on or alternately wait 30 seconds afterwards the Chromebook will then boot normally.
Another thing to try is doing a reset as described above, then pressing the refresh button and then tapping the power button, this is supposed to do a hard reset without entering recovery. I haven't tried this method yet, if my Chromebook acts up again I will give it a try and if it works I will update this post.