Screen is black and light is flashing blue, it wont shut off

[AC Question]

The screen is black, in the left top corner I have a blue light flashing. I have tried to shutdown phone using the power off button but I can't see screen to know what it saying

 

[Tim1954]

Call the phone from another one. If it rings, it's the screen, if it doesn't, it's the phone.
There should be no lights of any sort if the device is powered off unless it's connected to a charger.
If you long press the three buttons (volume up, home, power), you may be able to boot it up in recovery mode... If not, take it to a repair shop.