When you mean black Screen, is Complete black screen or there is something blinking or Logo in the startup? if you can see something in startup like a logo computer, some text or “Press something to access of boot to something” maybe is a corrupted Operating System or bad Hard Drive. A bad hard drive can cause slow booting too. If you have a live CD Linux Distribution you can try to boot up and see Hard Drive Details, If you dont have one, you can try removing the hard drive and see if you can see something on the screen.
If the computer war working really hard, and you hit it, a GPU or CPU ball soldering can happen, you can try a external monitor to check if is a component level issue.
1) Remove the hard drive and power on is you see “No Bootable Media” or goes directly to BIOS can be a Operating System or Bad Hard Drive.
2)If you have a live CD Linux Distro, and is booting up and Hard Drive Details are OK, probably is a Corrupted OS.
3)If you have more than 1 RAM Memories you can try only one, may is a bad RAM causing black Screen.
4)last and worse case, soldered ball in CPU or GPU.