How to fix the Blue LED error on some BlackBerry 10 devices running BlackBerry 10.3.120
Now that the BlackBerry 10.3.1 OS build is official, BlackBerry has acknowledged the "Blue LED" issue by including it on its Knowledge Base. According to BlackBerry, the issue could occur when the user chooses the Restart option after pressing the power button. It could also be caused by a long press of the power button, or when taking out and reinserting the battery.
The resolution starts by making sure that the latest version of BlackBerry desktop software is installed on your computer. You can make sure you have the latest build by going to www.BlackBerry.com/Blend. You then connect your BlackBerry 10 device to your computer using a micro USB cable. Once the phone is recognized by the computer, download BlackBerryFix.zip to the Desktop on the computer. Once it is downloaded, double-click on BlackBerryFix.zip to open the file. Then, double-click on BlackBerryFix.exe. When the BlackBerry Fix window appears, check to make sure that the PIN number for your phone is displayed. Click on Fix This Phone.
This should get rid of the Blue LED issue that has been wiping the data from unfortunate Q10 and Z10 owners for over three months now.
source: BlackBerry via Crackberry