You may be able to troubleshoot this by working within the office LAN, if
possible.
In the offices I work with, where workstations are joined to a domain, and
the Internet connection is always on--provided by a router or ISA Server
2000--I can reboot any workstation, or power (most of) them on remotely.
Remote Desktop is a service and is active before logon.
The Internet connection, if credentials are saved for a specific user,
rather than all users, may not be active, however. Say more about how the
office machines connect to the Internet and whether there's a domain or
simply a workgroup involved?