It's not only the SID change that can cause this problem. Abount once a week
every NT server changes its password for the domain authentication. Usually
the domain "remembers" the last password (don't know how long). 
So when you restore the registry, there's a gap between backup time and
system crash (or restore time). When a refresh of the domain password
happens during this time interval, the server is probably not recognized in
the domain any more.
In this case just delete and redefine the server to the domain (server
manager). When the server now is recognized by the domain - fine! When not,
you have to login as a local administrator and select the properties of
network neighborhood; put the server into a workgroup and back into the
domain; now it should work.

Good Luck,
best regards,
Michael