XPS 8700, replaced HDD, USB boot issues

I got this computer back in 2013. It worked great for a while, but it's been running slow lately. Still usable, though. Until last week. All of a sudden, instead of booting up, it showed a black screen reading.

No boot device available =
SATA 0: None
SATA 1: Installed
SATA 2: None
SATA 3: None
SATA 4: None
SATA 5: None
Strike the F1 key to retry boot, F2 to run the setup utility.

After messing with it for a while, and continuously getting that message even after resetting the BIOS settings, I figured that maybe the hard drive had gone bad. So I put a new one in. After that, the same message appeared, but it now says SATA 0: Installed.

So I figured I'd probably just need to reinstall Windows from a USB flash drive. I downloaded the Windows 10 installation tool (https://www.microsoft.com/en-us/software-download/windows10) and, as near as I can tell, configured it on a USB flash drive as instructed.

But when I insert that flash drive into the computer and reboot, I can hit F12 and the load options pop up, but there are no options under UEFI to load from the USB. If I switch to Legacy mode, I do see the Sandisk flash drive under the options, but if I select it and reboot, I get a message reading "Reboot and select proper Boot device or insert Boot Media in selected Boot device and press a key."

So I'm stumped. I was able to restore Windows via USB on a different computer a while back, and I don't remember running into any issues like this. Is my computer just messed up (beyond the hard drive) or am I doing something wrong?