AMD has no drivers for that card on that OS. You must use the basic driver Microsoft supplies.
The following Discrete AMD Radeon™ Graphics products support up to WDDM 1.1 and DirectX® 10.1:
- ATI Radeon™ HD 4000 Series /ATI Mobility Radeon™ HD 4000 Series Graphics
- ATI Radeon™ HD 3000 Series /ATI Mobility Radeon™ HD 3000 Series Graphics
- ATI Radeon™ HD 2000 Series /ATI Mobility Radeon™ HD 2000 Series Graphics
These graphics products must be installed using display driver version: 8.970.100.9001. This driver is provided as a courtesy and only available via Windows Update. Please enable Windows Update and allow it to detect and install the appropriate driver.
NOTE: ATI Radeon™ HD 4000
/ATI Mobility Radeon™ HD 4000, ATI Radeon™ HD 3000
/ATI Mobility Radeon™ HD 3000, and ATI Radeon™ HD 2000
/ATI Mobility Radeon™ HD 2000 Series Graphics reached peak performance optimization on October, 2013. No additional driver releases are planned for these products.
I've used the workaround posted by Andy in this thread Driver for ATI Mobility Radeon HD 4200 Series?
The idea is to install AMDs Legacy drivers for Windows 8.1 in the compatibility mode of Windows 10. It fixed the resolution with my dad's HP G62 notebook and AMD Radeon HD 4200.
Try this if you haven't found a solution yet. It worked for me.
I don't know if anybody has recommended this or not but I just happen to stumble into a very easy fix and it worked perfectly. I was trying to install Minecraft on an older computer that uses the ATI Radeon HD4200 and nothing would work for me. I tried downloading drivers from the ATI support page but that didn't work at all. Here's what I did. I went into Device Manager, expanded "Display Adapters" and right clicked on "ATI Radeon HD 4200". I then clicked on "Properties" and on the properties window I clicked the "Driver" tab. I then clicked on "Update Driver" and on the next window I chose "Browse my computer for driver software". On the next window I clicked on "Let me pick from a list of available drivers on my computer". I placed a check on "Show compatible hardware" and it gave me a list of drivers available for the graphics card. I chose the oldest driver and installed it and it worked for me. After all the time I wasted looking for solutions and the solution was right there just waiting for me to find. I hope it works for everyone else.