Screen on my compact laptop went black and I can only turn it on but have nothing but black
If the laptop comes on normally otherwise and is booting to Windows (you hear the normal startup sounds), look closely at the display and see if you can make out a faint image. It often helps to shine a flashlight on the display.
If the display is faint but present, you probably have a bad inverter board in the display. The inverter provides power for the display's backlight, and without the light the display still works but you can't see it. Inverter boards are available for most brands, they're not usually very expensive, and changing one isn't too difficult. A Web search for your brand and model and "replacement inverter" should turn up several sources. There are also YouTube videos showing how to replace the inverter in many kinds of laptops.
It's also possible the backlight itself is bad. If so, replacing the display is usually preferable to trying to replace the light. The light is built into the display and it's very difficult to replace without damaging the part or the display in the process. The display can be expensive, though.
If you're not sure that the computer is working, try starting it with an external monitor connected. If there's no display then, there's something wrong with the system board that's preventing the machine from starting up. Get that fixed, and it will probably fix the display trouble as well.