What's hapening is that you only have one IP address that's your ISP gave you..
A router provides several services,
1. NAT Network Address Translation, meaning you have one INTERNET address the world sees, but you can have thousands of INTRANET on your network.
2. DHCP, handing out internal IP addresses.
3. Firewall, keeping viruses, port scanners, bad people from seeing your internal network.
A switch is a piece of dumb plastic that connects computers.
I just got a $15 dollar 4-port router from Office Depot, on sale..
If you can't take back the switch, or want to make it more flexible, try this:
C=Computer
S=Port on the Switch
C1 to S1
C2 to S2
S3 to Router 1
RInternet/DSL Modem
This will seperate the switch from the router, in case the DSL/Cable modem can't reach the networking closet/server room.
If you want another room, just run another wire.
When a rainy day comes with a unused computer, get
Smoothwall, a Linux based firewall that allows remote access for free.