Restore the System State portion of the backup on another machine running W2K3 or Windows XP, choosing the "Single Folder" option for the "Restore files to" and picking some sensible "Alternate location" (like a directory you make for that purpose). You'll be warned about how this is an "advanced" feature and that not all files will be restore. For your purposes, that's fine.
You'll get back a lot of the "%SystemRoot%\System32" directory (a lot of DLL files, etc), and the registry, too.
From there, the instructions that Shial (who seems to look rather like SHODAN) posted are the right track. Fire up "REGEDIT", highlight "HKEY_LOCAL_MACHINE" in your local registry, then use the "File / Load hive..." option. Choose the file from the "Alternate location" corresponding to the part of the registry you want to extract data out of (these files have no extension):
- SYSTEM - HKEY_LOCAL_MACHINE\System
- SOFTWARE - HKEY_LOCAL_MACHINE\Software
- SECURITY - HKEY_LOCAL_MACHINE\Security
- SAM - HKEY_LOCAL_MACHINE\SAM
- DEFAULT - HKEY_USERS.Default
Choose any name you want when loading the hive, so long as it isn't a name that's already used under HKEY_LOCAL_MACHINE. You're "mounting" that hive into your live registry, not unlike mounting an NTFS volume under a directory (except that you don't have to make the registry key to mount the hive into like you would an NTFS mount point).
When you're done, unload the hive by highlighting the key where it's mounted (HKEY_LOCAL_MACHINE\whatever_name_you_chose) and doing a "File / Unload hive...".