There is no configuration required for the USB headers. I would disconnect the header and inspect the pins. If one is bent, then you may be able to straighten it very carefully. Unfortunately in my experience, more times than not, a fully bent pin will break when straightened.
You can check device manager for any errors on the USB hubs themselves. I'd also ask you to take a picture of the header and post that so we can take a look at it. One thing to keep in mind, the mouse is probably USB 2.0 or even 1. It's possible with a damaged header to get some functionality. It sounds like the header is damaged and that's why you're able to connect a mouse, but the drive gets power but it isn't detected.
A few USB3-to-SATA adapters do not supply enough power to the hard drive (especially 3.5" HDD), which shows as missing drive, random disconnects, or data errors. That can be avoided.
You can do the same data transfer test with a (low power) USB3 MicroSD card reader.
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