My laptop screen has gone black. What is wrong with it?

[Stewart Johnston]

When the hinge broke, you probably damaged the cable that goes to the screen. It can be replaced without costing too much.
Always shutting down is normally a symptom of it overheating - that can be cured by setting it on a hard surface, not your bed, cushions, etc.
Switch it off when not in use, make sure your anti-virus is up to date, don't install dodgy software, and take better care of it, that way you should get many years use out of it.
Alternatively, abuse it and replace it every 6 months, if you can afford to!