Display suddenly stopped working

I've had my Inspiron 137000 2 in 1 for 3 years now. Warranty is no more.

The screen has a crack across it so I have turned off the touch screen function. It has been like that for a year now and I haven't had any problems.

Today, I was working on my laptop, left the room for a minute and when I got back the screen was black. I guessed it had went into sleep mode but after pressing a random key to bring it back it did not react. 

Long story short, the fan was working like crazy, laptop was pretty hot, the screen was black and unresponsive and even if I held the power button for a long time, nothing changed. I even unplugged it and it kept going (the battery is pretty much dead, it only works for more than 10 minutes if it is plugged in). 

It's been now more than an hour and the yellow light indicating it's low on battery has been on, no response from the laptop. What is weird is that the caps lock key light won't turn on and the keyboard lighting won't turn on either so I guess it's not just an issue with the display (?).

Any ideas? Thanks