It could be that someone on your network has the SASSER worm, this wortm exploits avunerability in the LSASS.EXE (which has to do wit the logon process).
to stop the computer shutting down when it says shutting down.
press start -> run -> (then type) shutdown -a
if you look at the lasts that are running you may also find variants of the sasser worm.
they will have names ruinning around the same theme.
there is an update available from microsoft that can fix this vunerability, http://www.microsoft.com/technet/sec.../MS04-011.mspx
it's be a good idea to install a firewall, although if this is a LAN then you shouldn't really need internal firewalls. (unless they are departmental).
If internal firewalls are not viable you could also try removing external internet connections floppy drives and CD drives to stop the introduction and spread of virus infection.