Where are hard drives drivers stored on a PC?

First, we need to know what model laptop or desktop PC you have, and what model specs your Motherboards and HDDs are, when you say, Motherboard A and HDD A or Motherboard B and HDD B? What is the model number of the PC and the Motherboard A & B and the HDD A&B? As we can't give you any exact answer to your problems if we don't know this information. There are allot of guides on the web for "How To Fix “No Bootable Device” Error" so look at this guide as you have this problem.

If motherboard B is the same as motherboard B and the same with the HDDs then all the peripherals from Motherboard A should work like ram and cpu but, it could be that the ram was shorted and damaged and the cpu also or a gpu if you had that connected. Its very hard to advise you on anything if you don't give us model number and even photos as its very hard to figure out what is damaged and going on with your PC.

We really need more details as to just what hardware you are working with, both motherboards and both drives. It sounds like the first drive failed catastrophically, burning out components on the drive. Luckily it also looks like that didn't end up harming the motherboard. On the second motherboard it is likely using something like Intel Rapid Storage Technology, where the drivers aren't included in the base Windows installation. If that's the case you need to download the appropriate missing drivers from the motherboard manufacturer, extract them to your install flash drive, then when you get to that place in the install ask it to load the driver from the flash drive. It will then recognize the drive and allow the install to complete, including the needed drivers as part of the install.