This is primarily a desktop PC solution, but may be implemented in some notebook / laptop PC's as well. This depends on the laptop make & model. Very few laptops have an expansion slot for improved graphics cards, which is required for this fix.
If all the rest of the hardware on a PC checks out as Windows 10 compatible via a reading of the Windows 10 system requirements, and the hardware check tool from Microsoft, but your video controller is incompatible with Windows 10, you may be able to do this.
Background: Windows 10 has a boatload of new code in it so that it can adapt to the screen size of the device it is running on. This operating system may be implemented on smartphones, tablets, laptops, desktops, all-in-one PC's, or even smart TV's. It needs to be able to work on all sizes of screens.
Because of this, the graphics controller chip or card must be able to support the new code. Some graphics controllers are too old to support the software, at a hardware level. They simply can't run the necessary DirectX version. Devices that run Windows 10 for desktop editions must include a GPU that supports DirectX 9 or later, per Microsoft specifications for desktop operating system versions. Even with an updated driver, they just aren't capable of running it. Others are no longer supported by the manufacturer, so the necessary driver software will never be written.
Microsoft doesn't appear include graphics controller testing in their hardware check tool. You must manually investigate the compatibility of your Graphics Controller yourself. You'll need to look up what make and model of graphics controller your system has. Usually these can be found online. CNET.com is usually pretty good for PC specifications for many makes and models. The manufacturer website may also be a good resource.
Once you know what graphics controller your machine is using, you'll need to research online whether it is supported for Windows 10. Even if all the rest of your PC hardware meets all the Windows 10 system requirements, if your graphics controller is incompatible, upgrading is likely to cause you a lot of grief with hangs, freezes, and the dreaded blue screen of death. This is because instructions your graphics controller can't execute are coming in due to all that new code. This is also a big reason why early reviews of Windows 10 were so mixed. People loved it or hated it. That was probably a direct result of not knowing that they needed to check this manually before updating...
Once you have determined that the rest of your PC is able to run Windows 10, but your GC will not, what you can do is purchase an expansion card GC that is known to support Windows 10 and install it to a PCIe x16 slot or AGP slot on your machine. (Few laptops have these expansion slots available) AGP slots are pretty old, so it's unlikely, but never rule anything out.
This will replace the integrated GC on the CPU chip, or replace an existing incompatible expansion card GC. (Once you have the new graphics card thast you are certain supports Windows 10 installed and running, you should boot into the system BIOS/UEFI and disable the integrated graphics controller if it's present. It will be using up system RAM memory for nothing. That will slow your machine down a bit.
It takes a bit of research, but it's likely cheaper than a new PC.
I just did this myself by making one good Win 10 dektop out of two old ones that I am donating to my Civil Air Patrol squadron.
One PC had a compatible GC expansion card, the other had an incompatible integrated GC.
Temecool Computer Repair