This is a fairly common issue, and is either a hardware problem or a Windows boot problem. Some possibilities include: the laptop motherboard or display may have died, or a laptop component failed and needs to be replaced, your BIOS is corrupt, and possibly the Windows boot sector (or Windows itself) has gone corrupt. There are a few things you can do, which I will explain in detail below. Note that these steps apply to any version of Windows, and not just Windows 10.
How to Fix Laptop Black Screen, Windows Won't Boot
Here are a few things you can try:
First, unplug the battery from the laptop and then try and power on with only the power cord plugged in. If it works without the battery plugged in, then most likely your battery needs to be replaced. If you still have a black screen, keep the battery unplugged and proceed to the next step.
Unplug the power cord, turn the laptop over and take the hard drive out of the machine, then power the system back on again. If you progress past the black screen then there may be something wrong with the hard drive (or Windows), or your BIOS configuration which is causing some sort of lengthy delay. In the latter case you will need to go into the BIOS and review your boot sequence. In the former case you can try inserting another hard drive (if you have one) to see if you get past the black screen. If you do get past the black screen, then the problem is likely the other hard drive. If you don't have another hard drive you can try and boot from a Windows 10 USB / DVD (installation media) and attempt to install Windows 10 again. If it works after that, then the problem was indeed Windows. If none of that works, then proceed to the next step.
Unplug the power cord, turn the laptop over, then remove your RAM modules and put them back in. Before handling the RAM, make sure you touch a wall outlet (power socket) screw which is grounded and will help prevent static electricity. Tip: only touch the RAM by its outer edges - never touch the chips or the gold conductive parts or you will risk damaging the chip with potential static electricity. If the laptop has more than 1 RAM module, try plugging in one module at a time, then power on, test, and see if you get past the black screen. If not, proceed to the next step.
Another thing you can try is to re-flash the laptop's BIOS. Sometimes the BIOS goes corrupt and will give you a black screen - this happened to me with my Acer notebook, and re-flashing the BIOS worked. Since your computer won't even boot at this point, the only way you can re-flash the BIOS is if your laptop manufacturer supports flashing the BIOS during a power-on state. This is usually done by copying a BIOS .ROM file onto a USB flash drive, then you insert the flash drive into the laptop, then press a series of keys (example: FCN + ESC + Power Button, for example) to initiate a power-on flash. To figure out if this option is even available, you will need to go to the manufacturer's website, search for your laptop model, locate drivers and downloads, then look through the BIOS section for something matching what I just mentioned.
If none of that helps you can try bringing the machine to a computer shop. If you choose this option you might want to ask if the shop charges a diagnostic fee, first. If they do, then you will need to figure out if it's worth spending the money to perform tests on a possibly dead laptop, or to take the money and put it towards purchasing a new laptop. I suggest calling around, either way.
Also: if the hard drive is in working order, it is possible to retrieve data from the old laptop, then place it onto another machine, or even a new laptop. In either case, you will need to purchase an external 2.5" hard dive enclosure, insert your old drive into it, then attach it to another machine (or new laptop), then copy the files over. Once files are copied over you will need to reset file permissions (access rights) or the files won't open and may not be writable. I can help with this by remote desktop support if you need.
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