acer aspire 5560G screen does not turn on

Hi, i turned on my laptop and had blue screen on death appear. After turning off and back on ws asked to restore the laptop to the most recent working state. Which I did. Since then it has turned itself off and I can't get the screen to work. The blue power light is on.

I've tried taking the battery off, pressing on for 30 seconds to 1 minute, plugging in the power only, then returning the battery. I've checked the brightness, and Fn+F5 but still nothing. Not sure if there is anything I can do without taking it in for repairs? Of course, I havent backed up anything yet so I really don't want to lose the stuff I have on the laptop.