Make sure you downloaded the right version (32 bit vs 64 bit) for your operating system.
Your processor i5-4200U is listed among the supported ones on the Intel driver page.
OK, yes, that was a moment of genuine stupidity.
I downloaded the 64 bit version (both formats) and they gave me an error message saying "The driver being installed is not validated for this computer. Please obtain the appropriate driver from the computer manufacturer." I went on device manager, told it to update the driver software with the downloaded versions, and regardless of what I tried it claimed that the most up-to-date driver was already installed.
No idea where to go from here. Maybe I'll try a full driver reinstall.
EDIT: Did it. When I tried installing it said that my computer does not meet the minimum requirements for installing the software. Is the processor the only factor determining which driver you can use? Because if it isn't than it looks like I'm just out of luck.