USB3.0 driver Intel has tested and it work perfectly fine, since you have an AsRock motherboard your best support will be with them as they are more familiar with your motherboard, BIOS, software etc.
However, you can try the following:
Make sure you have the latest chipset driver (INF) installed from your motherboard manufacturer website, if it is already installed, try reinstalling it again. Try the AsRock driver first, if it doesn’t work you can try the Intel® generic driver, you can download it at:
Reinstall the Intel USB 3.0 driver ver: 22.214.171.124 driver. You can download from your motherboard manufacturer website and if the problem persists, you can try the Intel® generic version:
Check if there is a new BIOS version to update your motherboard BIOS and check with AsRock if there is any configuration that it needs to get done in the BIOS to have it work correctly with Windows®7 and USB3.0, usually there is a xHCI option in the BIOS that it needs to be enabled.
You can download the drivers for your motherboard here:
NOTE: This link is being offered for your convenience and should not be viewed as an endorsement by Intel of the content, products, or services offered there.
Make sure Windows is up to date with all the important updates available.
I hope this can help.
At this point, I strongly recommend contacting ASRock, they are more familiar with your system and they might have a solution for the USB 3.0 when installing Windows®7 with this computer, from my end, if you already tried the recommended troubleshooting above and the problem persists, then it could be that there is a configuration in the BIOS that you are missing or that the USB ports are not working properly and you will need to try to request a replacement from AsRock.
I found an easy workaround for my particular problem here: https://answers.microsoft.com/en-us/windows/forum/windows_7-hardware/computer-does-not-have-the-necessary-usb-software/8147d409-d076-49eb-8572-5631f9c5e1f8?db=5
TL;DR: move/rename/delete usbready.exe within the HP driver software and it'll just skip the USB detection and install the drivers without issues.
I messed with the driver files before but didn't think renaming usbready.exe would do the trick. Nice way to detect USB compatibility, HP; thankfully I'm not buying their stuff ever again.
Microsoft USB Fix It was no good either. It seems to detect USB controllers using Get-WmiObject Win32_USBController in one of its Powershell scripts; running this command in Powershell detects the xHCI controller, so either there are more checks or Microsoft messed up somewhere.
My particular setup of Windows 7 + Skylake + H110 + HP printer put me into this mess. Next time I'll teach my mom how to use Linux, it'll be less of a headache.