Laptop crashed last night + now won't turn back on

I was using my laptop last night when it froze and crashed - I got a black screen saying "your computer needs to restart" and I think I really messed up by turning my laptop off rather than letting it restart.

I've tried holding down the power button for 60 seconds with all cables removed then plugging them back in and trying to switch on, it isn't working. My laptop power light turns on and the fans start, but nothing pops up on my screen.

Any tips??