Stop in for a cup of coffee
FAT is corrupt, Maybe.....
That or a physically failed drive, be it electronically or mechanically either one.
Usually a corrupt system will work until it's rebooted and then not boot.
A lockup while in use is usually a failing drive.
I have linux discs that can be booted from and even get a computer back on the internet even with no HD at all, but no disc drive screws that.
The same can be done with linux on a USB drive.
Just got to know how to do it, because you have to download one of the linux ISO's and make a bootable device with that.