Find Device Manager in Control Panel and check your Display Adapters. If you can reinstall the drivers from Safe Mode all may be well. The graphics chips for laptops are nearly always soldered onto the motherboard so if it is damaged and isn't being recognized in Device Manager what you have now is as good as it gets. You'd need to replace the motherboard to fix the graphics. A new laptop could be a better decision.
The easiest way to find out what you have there is to reinstall Windows. When I do this for customers I usually recommend that we replace the internal spinning hard drive with a much faster, more reliable solid state drive (SSD). My fav. is the Samsung EVO 256GB or the 500GB 2.5" for laptops. Comes with a 5 year warranty and could run up to 5 times faster than the old drive (depending on how old your laptop is). If the laptop is 5 to 6 years old (or newer) then you are going to get good results. If it is older that 6 years, you might want to replace the whole thing anyways. Sometimes these accidents are timely and line up with the need to move up to a new model anyways? Luckily you can get in via Safe Mode and copy any data you want.
In the future: Have a good back up method like Microsoft's Synchtoy 2.1 running in "contribute" mode (that's the only safe way to use it for backup) or a Carbonite subscription (there are others, this is just one I am familiar with). When you have a good backup you won't hesitate to wipe your machine and reinstall Windows. =)
...replacing the motherboard or buying a new laptop is better? At least my solution gives that laptop a chance at a new life. The SSD can be pulled back out if it doesn't work and the original drive can even be put back in the rebuild isn't the fix.
Weighing cost is the thing if the motherboard is damaged. Replacing it is going to be expensive unless you have the time, expertise and patience for a DIY job. It's rare to hear back on the forum about how an issue was resolved - or not - but it would be nice to hear if it was an easy fix.