The basic reason for Last Know Good was to allow backups for things that are involved in booting your computer. This system was not booting, so the optionmay have helped the original problem, unless you know the Auto Repair has already tried that.
Basically there are five Registry hive files inside
"System32\Config" folder. They are
SYSTEM, SOFTWARE, DEFAULT, SAM and
SECURITY. Upon booting, Windows will read this hive files and build the Registry dynamically depending on the hardware and software configuration of the system.
SOFTWARE is the hive file which usually stores all software configurations and
SYSTEM will have all hardware and driver related info. Usually
SYSTEM will be mounted in the Registry branch
HKEY_LOCAL_MACHINE\SYSTEM. Under that branch there will be at least two sub branches named
Controlset001 and
Controlset002 etc. A control set contains system configuration information such as device drivers and services. Usually Windows will only use either one of the Controlset at a time and the other one will be used a s a backup.
What are Control Sets? What is CurrentControlSet?
For example, if you install a new driver, a configuration information for it will be written under the current Controlset in use - let us say "Controlset001". Suppose If the new driver install crashed your system and when you select "Last Known Good", Windows will read the backup Controlset which doesn't contain the new changes ( in this case "Controlset002" ). Since the backup "Controlset" is not updated with new driver's configuration, usually the system will boot fine so you can troubleshoot the issue.
I would be interested in knowing, when a user cannot access the Reset function during a Repair option, what does deleting the HKLM\System key do to suddenly allow such access? Why was it designed in such a manner, and does it work the same way in Windows 8.1?
As you already know, "Refresh" operation will preserve all installed drivers and modern apps. To do that the process must mount both SYSTEM and SOFTWARE hives and backup software and driver settings. Although "Reset" won't preserve anything, it will also try to mount the hives - may be because "Reset" and 'Refresh" are performed by same tool or "Reset" may trying to read licensing info to preserve activation status.
If one of the hive file is corrupted, the process won't be able to mount them and hence the operation will be failed. If we rename the hive files, "Reset" will skip the hive mounting process and continue the operation.
Sorry if this is confusing. I only barely speak English.