How do you find out what IP address was assigned to a windows machine, if all
you have is its hard drive, or a backup of its filesystem?

These settings are in the registry:

HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Tcpip\Parameters\Interfaces\{BD0FEE19-A63D-4844-A6F6-E9BD91AB8D85}

For an offline machine, grab the registry file from
WINDOWS/system32/config/system, then on another windows machine, regedit
click on HKEY_LOCAL_MACHINE
File > Load Hive...
load that 'system' file

Then, you probably won't have CurrentControlSet -- check each of the
ControlSet001, 002, etc. The IP settings are usually the same in all sets; if
not you'll have to work out which ControlSet was active.