Laptop - Black Screen when turning on?

Hello. My laptop was working pretty well last night, but at the end of the night it was starting to really blow out some hard air, when I wasn't even using it. It was next to me, left on as I was doing something else next to it, so when it starting blowing out air I closed the lid and after about 2 minutes it stopped. The next morning I opened the lid up, it had turned off, so I plugged the charger in and booted it up.

Much to my surprise it turned on, but the screen was completely black. I didn't hear any beeps, and the keyboard didn't light up and didn't respond to input. Although.. I heard the computer try and read the empty disc I had left in there, and the fan seems to be blowing out a little bit of hot air. The power button is circle, and it has a border, the border is the light around the button.. the light on the power button lights up when I turn it on. I then have 2 lights at the bottom of the laptop on the face of its bottom, the first light lights up when the charger is plugged in, the second light is meant to tell me if its turned on or off (the laptop) but now the second light never lights up, its always unlit?

What have I tried?

I tried turning it off, removing the power and battery, holding the power button for 60 seconds then putting the charging cable back in without the battery and booting it up. The first light at the bottom changed from orange (It lights Orange when the battery charger is plugged in) to white, I guess its Orange if the battery is in, white if its not? So I booted it up, and it just did the same old thing..

I am running on Windows 10, on a Toshiba Laptop.

I have also tried connecting it to my TV via HDMI but the television just shows a Blue screen with "No Signal", the Laptop also stays the same, black with no input on the screen.