Computer disappeared from Workgroup

Solution 1:

Computer browsing/network neighborhood is fairly unreliable w/out WINS and/or dynamic DNS. WINS is the easiest solution. Give the Server 2003 computer a static IP.
Add the WINS service to the Server 2003 computer.
In the scope of the DHCP server (probably the router or the Server 2003 computer) add the IP of Server 2003 computer for the WINS server.
Do an IP config /release & /renew on each of the other 7 computers, or reboot them.
If the router is doing DHCP and doesn't have an option for WINS in the scope then disable DHCP on the router, install DHCP service on the Server 2003.
Configure the DHCP scope w/ options for router, DNS server(s), WINS (0xh for the type).