I just experienced this on a 2014 ASUS AMI motherboard BIOS
None of my SATA HDD or SSD would turn up in the boot priority list. I would get Generic Storage Device on the top of the list, followed by USB HDD drives. The BIOS seemed to boot by testing all the drives present, and looking for an OS.
I assumed that my SSD was being misrepresented as this Generic Storage Device, so I thought my disk imaging backup/restore software had mangled the MBR or start sectors of the drive. But I couldn't figure out why all drives I put on SATA were like this, so I started suspecting I'd damaged the motherboard.
It took me a couple of hours to twig that the USB drives were being registered OK, but nothing I put onto SATA would be listed in the boot priority list. Eventually I pulled everything off SATA and USB, including the USB headers on the motherboard. The culprit turned out to be a wretched el-cheapo 5.25" USB front panel which was creating an illusionary Generic Storage Device, and somehow blocking the detection of everything else.
On my last 2009 mobo, I'd had quite a few boot jamming problems because of a lone USB storage device somewhere.