I don't recall having this issue in the distant past but nowadays at least Debian seems to be very picky about this.
I used dd to copy one hard drive to another and tried booting it. Everything seemed fine with grub working but each time it would drop to the busybox shell. There is no particular error so this is misleading.
Normally the first things you would check are to make sure your fstab is correct (that the UUID is correct)and that you've updated grub.&........